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Question: <p>Let <span class="math-container">$X \sim \operatorname{N}\left(0,1\right)$</span> be a standard normal distributed random variable:
Can someone please please show me the whole way how to find the density of <span class="math-container">$\left\vert X\right\vert$</span>.</p>
<p><em>My tries:</em> I saw sites... | https://math.stackexchange.com/questions/4163938/how-to-find-densitiy-of-x |
Question: <p>Let <span class="math-container">$A$</span> and <span class="math-container">$B$</span> be two events such that <span class="math-container">$\Pr[A\cap B]=0.2$</span> and <span class="math-container">$0.3<\Pr[\bar{A}\cap B]<0.4$</span>. Find <span class="math-container">$a,b\in\mathbb{R}$</span> such... | https://math.stackexchange.com/questions/4165711/from-pra-cap-b-and-pr-bara-cap-b-deduce-pra |
Question: <p>I'm trying to develop an algorithm for finding biased coins. The basic problem formulation is this:</p>
<ol>
<li>There are an infinite number of coins</li>
<li>Some proportion <span class="math-container">$t$</span> of the coins is biased (this number is known)</li>
<li>All biased coins have the same proba... | https://math.stackexchange.com/questions/4160412/finding-a-rare-biased-coin-from-an-infinite-set |
Question: <p>A bag contains 6 white balls, 5 black balls and 2 red balls.
If two balls are drawn at random, what is the probability that neither of them are white?</p>
<p>For this question, the method that I used was to consider the four possible cases, BB, RR, BR, RB.</p>
<p>Therefore <span class="math-container">$$P ... | https://math.stackexchange.com/questions/4165726/a-bag-contains-6-white-balls-5-black-balls-and-2-red-balls |
Question: <p>I study math many years ago (I am engineer) and not remember how exactly calculate probability for such problem. I choose n values from m set and want calculate probability that all will be unique, has <span class="math-container">$1$</span> repeat or less, <span class="math-container">$2$</span> repeats o... | https://math.stackexchange.com/questions/4166183/what-is-probability-of-choose-already-choosen-when-we-choose-n-values-from-set-l |
Question: <p>How do we show that if $\sum E(|X_n - X|^r) < \infty$ then $X_n {\to} X$ almost surely for $r > 0$?</p>
<p>I know that it's true for $\sum P(|X_n - X| > \epsilon) < \infty$, but how do we extend this to account for the $r$-th mean?</p>
Answer: <p>$\sum E(|X_{n}-X|^{r}) = E(\sum |X_{n}-X|^{r})... | https://math.stackexchange.com/questions/2770386/sum-ex-n-xr-converges-implies-almost-sure-convergence |
Question: <p>I recently did a question, Numbers are selected at random, one at a time from two-digit numbers {00-99} with replacement. An event E occurs if and only if the product of the two digits of a selected number is 18. If four numbers are selected, Find the probability that the event E occurs at least 3 times.</... | https://math.stackexchange.com/questions/4166345/use-of-binomial-probability-distribution-if-events-occur-simultaneously |
Question: <p>I'm stuck at solving the following problem: launch 3 fair coins independently. Let A the event: "you get at least a head" and B "you get exactly one tail".
Then what is the probability of the event <span class="math-container">$A \cup B$</span>?</p>
Answer: <p>Note that <span class="ma... | https://math.stackexchange.com/questions/4107396/coin-tosses-probability-to-calculate |
Question: <p><strong>Q.1)</strong> A family has $n$ children, $n\geq2$. We ask from the father, "Do you have at least one daughter named Lilia?" He replies, "Yes!". What is the probability that all of their children are girls? </p>
<p>In other words, we want to find the probability that all $n$ children are girls, giv... | https://math.stackexchange.com/questions/1893041/conditional-probability-what-is-the-prob-that-all-are-girls-given-that-there |
Question: <p>I was wondering, if you flip a fair coin $5$ times, whether you can calculate the probability of getting at least one head is calculated like this:</p>
<p>You can do the complement of getting at least one head which is TTTTT: $\dfrac1{2^5} =\dfrac1{32}$</p>
<p>Then you do $$1-\frac1{32}= \frac{31}{32}\;,... | https://math.stackexchange.com/questions/144499/probability-of-heads-in-a-coin |
Question: <p>I am trying to calculate the percentage of winning for a certain event but cannot find the right approach or an easier way to exclude special cases. </p>
<p>Problem::
In many Trading Card Games (TCG) players are given the option to enter tournaments that reward them based on the number of wins they can a... | https://math.stackexchange.com/questions/2972892/how-to-calculate-at-most-with-special-cases-removed |
Question: <p>I'm trying to understand the following question:</p>
<blockquote>
<p>An engineer conducts tests to find out if circuits of a certain type are prone to overheating. 30% of all such circuits are prone to overheating. If the circuit is prone to overheating, the test will report it is not prone to overheati... | https://math.stackexchange.com/questions/1737564/conditional-probability-question-understanding-mistake |
Question: <p>I'm new to probability and I'm currently studying its axiomatic definition. I'm having a real hard time trying to understand the following exercise:</p>
<p>"
Tomorrow there is an exam. Esther has studied really hard, and she only has <span class="math-container">$\frac 1 5$</span> probability of not pass... | https://math.stackexchange.com/questions/2978525/axiomatic-probability-intersection-formula |
Question: <p>Question: A fair coin is independently flipped <span class="math-container">$n$</span> times, <span class="math-container">$k$</span> times by <span class="math-container">$A$</span> and <span class="math-container">$n − k$</span> times by <span class="math-container">$B$</span>. Show that the probability ... | https://math.stackexchange.com/questions/2978537/showing-probability-that-a-and-b-flip-the-same-number-of-heads-is-equal-to-a |
Question: <p>If $q$ number of elements are scheduled only to stay together, without having any specific order, what would be the permutation of $r$ elements taken from $n$ elements?</p>
<p>For example, suppose we have 5 alphabets $A, B, C, E, F$. If A and E always stay together, how many permutations are possible if w... | https://math.stackexchange.com/questions/1495199/what-should-be-the-general-formula-for-the-following-permutation-problem |
Question: <p>How to show that without using Venn Diagram</p>
<p><span class="math-container">$P(A) + P\left( {\bar A} \right)P\left( {B|\bar A} \right) = 1 - P\left( {\bar A \cap \bar B} \right)$</span> ?</p>
<p>Effort so far</p>
<p><span class="math-container">$P(A) + P\left( {\bar A} \right)P\left( {B|\bar A} \right)... | https://math.stackexchange.com/questions/3832297/how-to-prove-that-pa-p-left-bar-a-rightp-left-b-bar-a-right-1 |
Question: <p>Recently, I encountered a probability question which can be phrased differently:</p>
<p>Q1: A letter is chosen at random from the word <strong>MISSISSIPPI</strong>. What is the sample space.</p>
<p>Q2: The letters from the word <strong>MISSISSIPPI</strong> are put into a bag. What is the sample space.</p>
... | https://math.stackexchange.com/questions/4044378/probability-question-on-sample-space |
Question: <p>A bit surprisingly I can't find the answer to exactly my question. I am looking for the formula to calculate at least k successes with n tries without replacement.</p>
<p>For example take the bag/balls problems. Let's say 250000 balls in the bag 250 white 249750 blue. If you draw 8500 balls what is the pr... | https://math.stackexchange.com/questions/1680387/at-least-k-successes-in-n-tries-without-replacement |
Question: <p>I see that there is a "fact" $P(A|B)=1−P(A^{c}|B))$, this can be deduced or what is the intuition? I can see that the "domain" is reduced in both cases to $B$ and that we use $A$ and $A^{c}$ and this makes sense I just don't know where to take this "fact" from.</p>
Answer: <p>$$\begin{align}\mathsf P(A^\c... | https://math.stackexchange.com/questions/2484262/proof-of-pab-1%e2%88%92pacb |
Question: <p>I am reliably informed that the probability of getting 3 of a kind in 5 rolls of a 6-sized dice is approximately <span class="math-container">$0.1929$</span>.</p>
<p>I'm assuming this excludes 4-of a kind and 5-of a kind but not full-house (3 of a kind plus two of a kind).</p>
<p>Trying to check this I r... | https://math.stackexchange.com/questions/3476371/3-of-a-kind-5-rolls-6-sized-dice |
Question: <p>If i have four dice i calculate the chances of getting at least one 2 as 864 ÷1296 = 66,66% since if on one dice a 2 comes up then it does not matter what comes up on the other 3 dice (1×6×6×6 possible outcomes × 4 times = 864), i still have thrown a two.</p>
<p>If i now work out the chances of not throwi... | https://math.stackexchange.com/questions/2980503/odds-of-winning-plus-odds-of-losing-do-not-equal-100 |
Question: <p>Given two cdf's <span class="math-container">$F_1, F_2\colon [0,1]\to\mathbb{R}$</span>, it is always possible to find two real-valued random variables <span class="math-container">$X_1, X_2$</span> such that <span class="math-container">$X_i$</span> is distributed according to <span class="math-container"... | https://math.stackexchange.com/questions/4172926/inherently-independent-distributions |
Question: <p>The taxi driver drives through four villages <span class="math-container">$W,Z,X,Y.$</span> These roads form a quadrangle where <span class="math-container">$WX = 5, WZ = 10, ZY = 5$</span> and <span class="math-container">$XY = 10.$</span> With a probability of <span class="math-container">$\dfrac{1}{4},$... | https://math.stackexchange.com/questions/4163648/one-problem-about-the-villagesprobability-theory |
Question: <p>Three spinners are marked with equal amounts of Red, Blue and Yellow. At a particular instance, all three are spun together. What is the probability that at least two of the spinners land on red?</p>
<p>The at least part is confusing me.</p>
<p>My attempt:
So if all three lands on red the probability will ... | https://math.stackexchange.com/questions/4171461/what-is-the-probability-that-at-least-two-spinner-land-on-red |
Question: <p>An urn contains <span class="math-container">$4$</span> blue and <span class="math-container">$4$</span> red marbles. At first a marble is drawn (without looking) and removed from the urn. Then, a marble is drawn from the urn, its color recorded and put back in the bag. This process is repeated <span clas... | https://math.stackexchange.com/questions/4174914/drawing-without-replacement-problem-formally-specifying-the-probability-space |
Question: <p>So this is an example straight from a book, like an example to help teach the material yet it makes absolutely no sense or I am just not seeing where they make the jump at.</p>
<p>We have the following: Consider the experiment consisting of 2 rolls of a fair 4-sided die. Let X be a random variable, equal ... | https://math.stackexchange.com/questions/2159690/what-is-the-prx-x |
Question: <p>I am solving the following probability exercise. The solution I have found is very counter intuitive and I feel It is wrong, but I can't seem to understand why.</p>
<p>A fair coin is tossed twice, you have to decide wheter it is more likely that two heads
showed up given that: 1) at least one toss is head,... | https://math.stackexchange.com/questions/4174777/coin-tossing-whats-more-probable |
Question: <p>When we write <span class="math-container">$X\stackrel d= Y$</span>, does this mean that <span class="math-container">$X$</span> and <span class="math-container">$Y$</span> have exactly the same distribution?</p>
<p>For example, <span class="math-container">$X\sim\mathcal N(\mu,\sigma^{2}) \ \text{and}\ X\... | https://math.stackexchange.com/questions/4086903/x-stackrel-d-y-what-does-it-exactly-mean |
Question: <p>Is there any way of analytically determining the expected value of <span class="math-container">$Z=e^{\alpha X e^{\beta X}}$</span>, where <span class="math-container">$X\sim\mathcal N(0,1)$</span> and <span class="math-container">$\alpha,\beta$</span> are known constants?</p>
<p><strong>A couple of the me... | https://math.stackexchange.com/questions/4176572/expected-value-of-the-exponential-of-a-normal-lognormal-mixture-in-the-special-c |
Question: <p>If four people are in a room for 1 hour, each on their own very old laptop and each laptop has a 10% chance of crashing during that time, then I thought the probability of at least one laptop crashing would be:</p>
<p>1/10 + 1/10 + 1/10 + 1/10 = 2/5</p>
<p>But then if the chance of crashing was 25% it wo... | https://math.stackexchange.com/questions/2988464/basic-probability-of-at-least-one-independent-event-happening |
Question: <p>I have the following question, but I fail to get the right answer. There are two boxes - box <span class="math-container">$A$</span> and box <span class="math-container">$B$</span>. Box <span class="math-container">$A$</span> has <span class="math-container">$5$</span> red balls and <span class="math-conta... | https://math.stackexchange.com/questions/4177140/probability-picking-up-from-a-box |
Question: <p>If say 2 people individually had a .05 chance of survival, 2 individually had a .10 chance of survival, and 2 individually had a .20 chance of survival (pulled these numbers out of a hat)</p>
<p>What is the chance that the family has more than 3 deaths.</p>
<p>The method I have is quite tedious and I was ... | https://math.stackexchange.com/questions/4177704/what-is-the-probability-that-you-have-more-than-3-deaths-in-an-infected-family-o |
Question: <p>I have a fold up table at home with six legs and three areas. Each area takes 2 legs to keep the table up, but when stored three legs are positioned on the left and three on the right.</p>
<p>Everytime I setup the table I randomly take the three legs on the left, put two on the left side and one in the mi... | https://math.stackexchange.com/questions/3379150/probability-each-table-leg-was-in-each-spot |
Question: <p>I fail to see what I have done wrong solving the following problem:
Consider a system with 3 parts A,B,C. Part A works with probability 0.8, part B with 0.8 and part C with 0.9 (they are independent). The system is considered to work only if there are at least two parts working. I wish to calculate what th... | https://math.stackexchange.com/questions/4180245/conditional-probability-a-system-with-3-parts |
Question: <p>Shuffle a standard deck of cards and cut it into three piles. What is the probability that a face card will turn up on top of one of the piles? </p>
<p>There are 12 face cards (four jacks, four queens and four kings) in the deck.</p>
Answer: <p>As has been mentioned in the comments, the split into three ... | https://math.stackexchange.com/questions/1415911/classical-probability-and-combinatorics |
Question: <p>My brother brings a certain number of his marbles to play with in my room. Each marble is distinct. He has 8 total marbles that are either red or blue. One day, I spotted two red marbles in my room. The probability that any two of his marbles (of those that he plays in my room), randomly chosen, both being... | https://math.stackexchange.com/questions/3397057/probability-and-marbles |
Question: <p>Consider families with two children, in which both parents have been identified as carriers of an autosomal recessive allele (Aa). At least one of the children shows the corresponding phenotype. When adding all the children of such families, what proportion of them will show this phenotype?</p>
<p>Why is t... | https://math.stackexchange.com/questions/4139143/genetic-combination-exercise |
Question: <p>There is the following question: There is a coin with probability <span class="math-container">$p$</span> to be <span class="math-container">$H$</span> and <span class="math-container">$q$</span> to be <span class="math-container">$T$</span>. I'm asked what is the expectation of the tossing number, conside... | https://math.stackexchange.com/questions/4182140/law-of-total-expectation-a-toss-of-a-coin |
Question: <p>I am interested in learning deeper about the number 1.96 used in the test of 95% confidence with a normal distribution. </p>
<p>More specifically, I am interested in whether someone could provide a numerical example of this, and how 1.96 is calculated using the 97.5th percentile, or anybody knows somewher... | https://math.stackexchange.com/questions/3336298/1-96-and-the-standard-normal-distribution |
Question: <p>I have a bag that contains coins, these coins could be biased coins, and each coin has a certain pre-determined probability of head/tail (independently of the other coins). This pre-determined probability is derived from a uniform distribution over <span class="math-container">$[0,1].$</span></p>
<p>I dra... | https://math.stackexchange.com/questions/358904/biased-coins-that-are-uniformly-distributed |
Question: <p>I'm having some trouble with this problem</p>
<blockquote>
<p>Suppose you flip a biased coin until a head appears. The coin has a $75%$ chance of coming up tails. Let $n$ be the number of flips that you need to do. What is the probability of the following events:</p>
<p>a) $n$ is at most $3$?</p>
... | https://math.stackexchange.com/questions/1216842/flip-a-biased-coin-until-a-head-appears |
Question: <p>So, I'm going to reformulate the problem because I think I did a bad job in the title because of the word limit:<br/>
We have 8 coins in a box - 1 has "heads" on both sides and the remaining 7 are normal. We pick 1 coin randomly and toss it 7 times. If we got "heads" all 7 times, what i... | https://math.stackexchange.com/questions/4183975/what-is-the-probability-we-picked-a-fake-coin-if-we-have-7-proper-and-1-with-hea |
Question: <p>I am confused about this. Do we need to consider in the factor of household distribution in the world?</p>
<p>The context is the movie <em>Avengers: Infinity War.</em> The important part of the question is a movie spoiler:</p>
<blockquote class="spoiler">
<p> At the end of the movie, Thanos gets all si... | https://math.stackexchange.com/questions/2875086/what-is-the-probability-that-a-random-family-of-4-gets-wiped-out-by-thanos-i-e |
Question: <p>I would calculate it as this <span class="math-container">$\frac{10^4-9^4-9^4+8^4}{10^4}$</span>. But it may be incorrect Because I summing the <span class="math-container">$10^4-9^4$</span> and <span class="math-container">$9^4-8^4$</span>. Is it the correct? </p>
Answer: <p>Let's consider "common digits... | https://math.stackexchange.com/questions/3502794/probability-that-two-plates-with-numbers-ranging-from-0001-9999-have-at-least |
Question: <p>An urn of 4 balls with 2 colors. Pick 2 balls and place them back 4 times. What's the probability of picking 2 balls of the same color twice in a row?</p>
<p>So the probability of picking 2 balls of the same color is <span class="math-container">$2\choose1$$2\choose2$</span>/<span class="math-container">$... | https://math.stackexchange.com/questions/3509877/an-urn-of-4-balls-with-2-colors-pick-2-balls-and-place-them-back-4-times-what |
Question: <p>In a horse race there are 10 horses. Bob wants to make a "trifecta Box bet". A trifecta box bet is when you choose the first three horses that finish the race in ANY order.
What is the probability to win a single trifecta box bet assuming every horse has equal chances to win.</p>
<p>My solution:
<span cl... | https://math.stackexchange.com/questions/3534016/probability-of-trifecta-box-bet |
Question: <p>All fair coins.</p>
<p>You pick 2 out of the bag and look at them, they are all heads.</p>
<p>So what is the probability of it?</p>
<p>I made a table under but it does not seem to work.</p>
<pre><code>A = Coin #1, B = Coin #2, C = Coin #3, D = Coin #4.
A B C D
1 H H H H ... | https://math.stackexchange.com/questions/3536847/probability-of-picking-out-two-heads-in-a-bag-of-four-coins |
Question: <p>A weekly lottery consists of 3 numbers drawn from the digits 0 through 9 with no repetition of digits. The first prize goes to the person with the correct sequence. Second prizes go to people with the correct digits in some other sequence. You buy a ticket.</p>
<p>a) What is the probability of winning the... | https://math.stackexchange.com/questions/3546985/what-is-the-probability-of-winning-first-prize-given-the-following-information |
Question: <p>Friends, I found trouble understanding this sentence. This is an exercise from a homework on The Central Limit Theorem. Can someone explain what this question is trying to ask? Much thanks. </p>
Answer: <p>Let <span class="math-container">$X_i$</span> be the number of eyes showing on the <span class="math... | https://math.stackexchange.com/questions/3601681/a-die-is-thrown-1000-times-find-the-limits-within-which-the-number-of-eyes-comi |
Question: <p>im trying to find a mathematical way to calculate the percentage chance that there is at least 1 Cheater in any given match chosen at random.</p>
<p>Game has 100 players per match</p>
<p>Total Players (including the Cheaters): 3000</p>
<p>there are 3 scenarios needing to be tested, a group of 500, 100, 25 ... | https://math.stackexchange.com/questions/4047746/probability-of-at-least-1-person-in-group-a-being-in-a-group-of-x-size-with-a-ge |
Question: <p><strong>Question</strong>: How many times should we throw a die if we want that the sum of points obtained
was at least 4500 with probability <span class="math-container">$p \geq 0; 975?$</span>
(use the central limit theorem).</p>
<p>I know that the probability of getting a given value for the total on t... | https://math.stackexchange.com/questions/4137950/probability-of-throwing-a-die |
Question: <p>I'm in grade 10, and I've just started to learn about complementary events. I am rather perplexed with this question. Isn't this question kinda contradictory, since <span class="math-container">$P(A) + P(A') = 1$</span>?</p>
<p>This is what I got to:</p>
<p><span class="math-container">$P(A) + P(B) = 1$<... | https://math.stackexchange.com/questions/3160157/by-means-of-an-example-show-that-pa-pb-1-does-not-mean-that-b-is-th |
Question: <p>Say I have <span class="math-container">$S_n = X_1 + X_2 +...+X_n$</span> where <span class="math-container">$X_i \sim Ber(1/2)$</span>. Then:
<span class="math-container">$$\lim_{n\to\infty}P(|S_n-\frac{n}{2}|<\frac{\sqrt n}{2})\implies \lim_{n\to\infty} P(|M_n-\frac{1}{2}|<\frac{1}{2\sqrt n}) \to 0... | https://math.stackexchange.com/questions/4187056/something-unclear-about-central-limit-theorem-law-of-large-numbers |
Question: <p>You are a military executioner tasked with eliminating some of the most dangerous criminals on Earth. You are handed 100 such criminals for immediate termination. However, just as you are about to execute them, word comes from a highly reliable source that 1 of the 100 is not a criminal at all. In fact he ... | https://math.stackexchange.com/questions/1832020/the-executioner-conundrum |
Question: <p>In Casella and Berger, the definition of almost sure convergence of <span class="math-container">$\{X_n\}$</span> to <span class="math-container">$X$</span> is</p>
<p><span class="math-container">$$P(\lim\limits_{n \rightarrow \infty}|X_n - X| < \epsilon) = 1$$</span></p>
<p>for all <span class="math-co... | https://math.stackexchange.com/questions/4187882/definition-of-almost-sure-convergence-from-casella-berger |
Question: <p>If I have a coin then chances of getting a <span class="math-container">$head$</span> or a <span class="math-container">$tail$</span> is <span class="math-container">$50-50$</span>. But why don't we take in account the case where coin is neither head and tail, where coin is standing upright, or it is makin... | https://math.stackexchange.com/questions/3506173/a-question-related-to-probability |
Question: <p>How can I find the probability of waking up at a precise minute? Say I fall asleep at $10$ PM and wake up at $6:01$ AM. There's a total of $481$ minutes we are dealing with so the odds of waking up at an exact minute would be $1:480$ right? And the probability would be $0.2$% ($1/481$), correct? But what a... | https://math.stackexchange.com/questions/2080754/how-can-i-find-the-probability-of-waking-up-at-a-precise-minute |
Question: <p>A random number generator generates a number between 0-9. Single digit, totally random. </p>
<p>We have the list of previous digits generated. </p>
<p>I would like to calculate what is the probability for each number between 0-9 to be the next number generated. </p>
<p>So we have something like: 0,2,3,4... | https://math.stackexchange.com/questions/2082137/probability-of-the-next-random-number-based-on-previous-numbers |
Question: <p>Take a look at this document: <a href="http://hal.in2p3.fr/in2p3-01082914v2/document" rel="nofollow noreferrer"><em>Functions of random variables</em>; Abdel-Hamid Soubra, Emilio Bastidas-Arteaga</a></p>
<p>In the section <strong><span class="math-container">$2.2$</span></strong>, they have given an examp... | https://math.stackexchange.com/questions/2932875/example-of-function-of-a-single-random-variable |
Question: <blockquote>
<p>A bin has $2$ balls, one is black and one is white. Every round a uniformly chosen ball is drawn from the bin. If the color of the ball is white, then the ball is returned to the bin with an additional white ball. If the ball is black the experiment is over. Let $X$ be the number of rounds i... | https://math.stackexchange.com/questions/2795511/what-independent-events-actually-means |
Question: <p>Link for the description: <a href="http://us.battle.net/hearthstone/en/blog/20324471/introducing-heroic-tavern-brawl-10-17-2016" rel="nofollow">http://us.battle.net/hearthstone/en/blog/20324471/introducing-heroic-tavern-brawl-10-17-2016</a></p>
<p>Lest assume that you build a very good deck with 60% winra... | https://math.stackexchange.com/questions/1972993/what-is-the-probability-of-winning-hearthstones-heroic-tavern-brawl |
Question: <p>There are 6 white beads and 5 black beads in your pocket. You randomly pull the beads one by one out of your pocket and place them on a table. Probability that the third bead drawn is the first white.</p>
<p>Now the solution is : the prob.of drawning 1st black bead (5÷11) × the prob.of drawing 2nd black be... | https://math.stackexchange.com/questions/4190549/confusion-in-identifying-independent-events |
Question: <p>Flip a coin repeatedly. Let <span class="math-container">$E_s$</span> be the number of coin flips it takes before seeing <span class="math-container">$s$</span> heads in a row. What is <span class="math-container">$P(E_s=n)$</span>? Specifically, I am concerned with <span class="math-container">$P(E_4=E_3+... | https://math.stackexchange.com/questions/3022791/probability-that-first-s-heads-in-a-row-occurs-after-n-flips |
Question: <p>So I would like to know the probability of the following scenario to happen.</p>
<p>I am from India. Jane(say) is from Brazil. I moved to Canada to work four months ago and have been hopping from one airbnb to another. Jane moves from Brazil to Canada to study and happens to be in the room next to me in t... | https://math.stackexchange.com/questions/2898661/probability-of-two-people-from-two-different-countries-meeting-in-a-different-co |
Question: <p>Assume a table with dimensions <span class="math-container">$n$</span>x<span class="math-container">$n$</span>. In each of the <span class="math-container">$n^2$</span> spaces, a random number (<span class="math-container">$m$</span>) such that <span class="math-container">$m\in\mathbb{N}$</span> and <span... | https://math.stackexchange.com/questions/4156924/probability-of-random-numbers-in-a-table-summing-to-10 |
Question: <p>Imagine this. Robert goes on vacation. Upon his arrival at the destination, he is unexpectedly greeted by a good friend of him, Jeremy. Weirdly enough, they happened to go on the same trip, be neighbors at the site, at the same time and place, and for the same duration. Keep in mind, none of them knew of t... | https://math.stackexchange.com/questions/4191840/how-would-someone-go-about-calculating-the-probability-of-the-unlikely-scenario |
Question: <p>My wife left on a business trip this morning. 20 people from the same company caught two consecutive flights. Each person checked in independently, yet my wife ended up sitting next to the same colleague on both flights!</p>
<p>What are the odds?</p>
<p>Assume both aeroplanes had 150 seats, in 3+3 config... | https://math.stackexchange.com/questions/2903649/what-are-the-odds-of-sitting-next-to-the-same-person-on-two-flights |
Question: <p>How can you solve conditional probability without formula - simply by logic and intuition?</p>
<p>For example, this problem has been circulated here and we all know the formal way to do it. Could anyone show how to logically solve it?</p>
<p>At a workplace 1% of the staff where injured during a year. 60%... | https://math.stackexchange.com/questions/2904005/solving-conditional-probability-without-formula |
Question: <p>If there is a 1 in 8 chance of an event and there is a further 25% reduction in this event happening what is the answer expressed in terms of 1 in X chance?</p>
<p>My first calculation I worked out as 1 in 32.
0.125 x 0.25 =0.03125</p>
<p>Then 1 in 12 (more guesswork) and then 3 in 32
0.125 x 0.25 = 0.... | https://math.stackexchange.com/questions/2907512/1-in-8-chance-of-an-event-decreases-by-25-what-is-it |
Question: <blockquote>
<p>Suppose we have a bag containing $m$ white and $n$ black caramels. We pic a caramel and if it is white, we eat it, otherwise we put it back in the bag. If we take out $r$ black caramels succesively, then we believe that we have eaten all the white caramels and we throw the bag. What is the d... | https://math.stackexchange.com/questions/2907888/distribution-of-white-caramels-thrown-away-from-a-bag-of-white-and-black-caramel |
Question: <p>Let X and Y be jointly continuous with joint probability density function<br>
$$f_{X,Y}(x,y)=\frac{1}{x},0\leq y\le x\le1$$<br>
Find the pdf of $Z=X+Y$ </p>
<p>Here is my solution:<br>
$$F_Z(z)=P(Z\leq z)=P(X+Y\leq z)$$<br>
$$=\int_{-\infty}^{\infty}P(X+Y\leq z|X=x)f_X(x)dx$$<br>
$$=\int_{-\infty}^{\inft... | https://math.stackexchange.com/questions/2908104/find-the-pdf-of-z-xy |
Question: <p>If someone gets $13$ mails over the period of $5$ weekdays. What is the probability that he gets at least one mail in each day?</p>
Answer: <p>HINT - I would say:</p>
<p>If number of solutions of the equation $i_1+i_2+i_3+i_4+i_5 = 13$</p>
<ul>
<li><p>where $i_1,i_2,i_3,i_4,i_5\in (1,2,3,\cdots,13) = \o... | https://math.stackexchange.com/questions/2912079/what-is-the-probability-that-he-gets-at-least-one-mail-in-each-day |
Question: <p>Imagine I have a real random variable $X$ with some distribution (continuous, discrete or continuous with atoms)</p>
<p>Now Imagine I have i.i.d. copies $X_1,...,X_n$, all independently and equally distributed as $X$</p>
<p>My claim is:</p>
<p>$$\mathbb{P}(X_2>X_1)=\mathbb{P}(X_2<X_1)$$
My secondy... | https://math.stackexchange.com/questions/2913017/is-it-true-that-the-probability-for-both-events-is-always-equal-if-yes-how-to |
Question: <p>I am struggling with this interview prep question... SOS</p>
<p>Two players pick cards from standard 52 card deck without replacement: 1st player
picks a card, then 2nd, then again 1st, then 2nd etc. They stop once somebody picks a king (of any suit),
the player who picks the king wins. What is the probab... | https://math.stackexchange.com/questions/2916365/two-players-pick-cards-from-standard-52-card-deck-without-replacement |
Question: <p>This is related to my previous question <a href="https://math.stackexchange.com/questions/2920891/find-the-number-of-ways-of-constructing-8-using-three-distinct-integers-from">here</a>.</p>
<blockquote>
<p>The numbers $0, 1, 2, 3, \ldots , 8$ are written on individual cards and placed in a bag. Three ca... | https://math.stackexchange.com/questions/2920913/is-the-following-probability-question-ambiguous |
Question: <p>There exist 7 doors numbered in order from 1 to 7 (going from left to right). A mouse is initially placed at center door 4. The mouse can only move 1 door at a time to either adjacent door and does so, but is twice as likely to move to a lower numbered door than to a higher numbered door each time it mov... | https://math.stackexchange.com/questions/2924838/cat-mouse-probability-question |
Question: <p>I have collected data on the time duration between consecutive occurrences of a particular event ("success"), and the amount of time between consecutive "successes" (in days) seems to be distributed using a Gamma distribution. Intuitively, this is not a Bernoulli trial because the probability of a "succes... | https://math.stackexchange.com/questions/2925412/probability-of-next-occurence |
Question: <p>Bill gave exams for the entrance at some specific gymnasium. <span class="math-container">$602$</span> students took part, which were classified, after the exams, in an ascending order, and the first <span class="math-container">$108$</span> students will be taken, which will accept to enter. Every studen... | https://math.stackexchange.com/questions/2929025/entrance-at-gymnasium |
Question: <blockquote>
<p>A point is chosen uniformly at random inside the triangle with vertices at <span class="math-container">$(0, 0), (0, 1)$</span> and <span class="math-container">$(1, 0)$</span>, meaning that the probability that the point lies in a certain region inside the triangle is proportional to the ar... | https://math.stackexchange.com/questions/2932126/density-of-a-random-variable |
Question: <p>A group of $2n$ boys is to be divided into two groups of $n$ boys . What is the probability that the two tallest boys are in different groups ? </p>
<p>This is how I attempted it: </p>
<p>The probability that the two boys are in same group can be obtained as follows:</p>
<p>First we separate those two p... | https://math.stackexchange.com/questions/2936889/probability-of-dividing-boys-in-2-groups |
Question: <p>Suppose we play a game where we roll a six-sided die. If a <span class="math-container">$4$</span>, <span class="math-container">$5$</span>, or <span class="math-container">$6$</span> is rolled, I get <span class="math-container">$1$</span> point. If a <span class="math-container">$1$</span>, <span class="... | https://math.stackexchange.com/questions/2937271/probability-of-winning-die-game |
Question: <p>Let (Ω, <span class="math-container">$\mathcal{F}$</span>, <span class="math-container">$\mathbb{P}$</span>) be a probability space and, for each t ∈ [0, 1], let <span class="math-container">$X_t$</span> be a random variable on (Ω, F, P). For <span class="math-container">$\omega \in \Omega$</span></p>
<p>... | https://math.stackexchange.com/questions/2938028/lim-sup-as-a-random-variable-in-a-bounded-interval |
Question: <p>I am helping a friend with a study guide for a class, and one of the problems is asking about the theoretical mean and standard deviation. Two 8-sided dice with equal probabilities for 1, 2, 3, 4, 5, 6, 7, and 8, are rolled, and the sum of the two dice are recorded. </p>
<p>So I have a dataset that is the... | https://math.stackexchange.com/questions/2941691/standard-deviation-of-two-8-sided-dice-rolled-10000-times |
Question: <p>n white and k black balls are randomly and independently distributed amongst m boxes. There is no limit to the number of balls a box can contain.</p>
<p>As a result, there are four possible states for each box:</p>
<ol>
<li>Empty</li>
<li>black only</li>
<li>white only</li>
<li>black and white</li>
</ol>... | https://math.stackexchange.com/questions/2949935/n-white-and-k-black-balls-in-m-boxes-probability-of-co-occurence |
Question: <p>Let <span class="math-container">$\theta_n$</span> be a random variable that can be <span class="math-container">$\{\frac{1}{n},\frac{2}{n},...,\frac{n}{n}\}$</span> with equal probability <span class="math-container">$\frac{1}{n}$</span>. My question is where does <span class="math-container">$\theta_n$</... | https://math.stackexchange.com/questions/2952037/let-theta-n-be-a-random-variable-that-can-be-frac1n-frac2n |
Question: <blockquote>
<p>What numbers in the interval <span class="math-container">$[0,1]$</span> can be generated by tossing a
fair coin? By generating a number using a coin, we mean finding an event that its probability is the given number.</p>
</blockquote>
<p>I think that any number in <span class="math-conta... | https://math.stackexchange.com/questions/2953555/what-numbers-in-0-1-can-be-generated-by-tossing-a-fair-coin |
Question: <p>Is there a nice rule describing how the values of <span class="math-container">$P(C|B)$</span> and <span class="math-container">$P(B|A)$</span> jointly constrain <span class="math-container">$P(C|A)$</span>? In particular, if I know that both <span class="math-container">$P(C|B)$</span> and <span class="ma... | https://math.stackexchange.com/questions/2957640/transitive-conditional-probability-constraints |
Question: <p>How can I solve this one? Ten cats are on the chessboard, every cat is on one of the square and the can be on the same square as well as in a different square. Every turn each cat jumps to the adjacent square with equal probability. They won't jump outside the board. So in the corner a cat can jump to thre... | https://math.stackexchange.com/questions/2957812/how-many-turns-it-takes-to-cats-in-a-chessboard-jumps-to-the-same-square |
Question: <p>Say that Amy tosses a coin 6 times, and Bob tosses a coin 5 times. What's the probability that Amy gets more heads than Bob does? </p>
Answer: | https://math.stackexchange.com/questions/2965489/probability-that-amy-gets-more-heads-than-bob |
Question: <p>We are playing with two dice until we get <span class="math-container">$10$</span> as the sum of the results two times in a row.</p>
<p>(i) What is the probability of having gotten this in <span class="math-container">$8$</span> throws?</p>
<p>(ii) What's the probability of having thrown a sum less than ... | https://math.stackexchange.com/questions/2965715/what-is-the-probability-of-obtaining-a-sum-of-10-in-two-consecutive-throws-of |
Question: <p>If <span class="math-container">$\exists k>1$</span> odd such that <span class="math-container">$E(X-E(X))^k=0$</span>, then is X symmetric?</p>
<p>I know that the converse is true, in fact, if X is symmetric, then all odd moments will be zero.</p>
Answer: <p>You can find a real-valued random variable... | https://math.stackexchange.com/questions/2967381/if-exists-k1-odd-such-that-ex-exk-0-then-is-x-symmetric |
Question: <p>A and B draw coins in turn without replacement from a bag containing <span class="math-container">$3$</span> dimes and <span class="math-container">$4$</span> nickels. A draws first. It is known that A drew the first dime. Find the probability that A drew it on the first draw.</p>
<p>I know that the proba... | https://math.stackexchange.com/questions/2969428/find-the-probability-that-a-drew-it-on-the-first-draw |
Question: <p>I'm not sure what field of math this is, I'm just interested in mathematics in daily life, here's a question that kept me thinking:</p>
<p>Lets say for a range between <span class="math-container">$1$</span> to <span class="math-container">$200$</span>, I randomly pick a number, for example I pick <span c... | https://math.stackexchange.com/questions/2976252/probability-of-arriving-at-a-number-after-a-certain-number-of-tries-with-the-fol |
Question: <p>Suppose we have code with <span class="math-container">$𝑛 = 100$</span> pages. The variable <span class="math-container">$𝑋𝑖$</span> is the number of errors on the page that is distributed Poisson meets the average of 1. Also, the number of errors per page is independent of the other page. Number The to... | https://math.stackexchange.com/questions/2982204/normal-approximation-to-poisson-problem |
Question: <p><span class="math-container">$$\mathbb P\{X\leq x\}=\int_{\Omega }\boldsymbol 1_{X^{-1}(-\infty,x]}(\omega )d\mathbb P(\omega )=\int_{\Omega }\boldsymbol 1_{(-\infty,x]}(X(\omega ))d\mathbb P(\omega ),$$</span></p>
<p>how can I continue ? I guess I have to do the substitution <span class="math-container">... | https://math.stackexchange.com/questions/2984419/how-can-i-prove-that-mathbb-p-x-leq-x-int-inftyx-f-xtdt |
Question: <p>I have difficulty to understand random variable. Let <span class="math-container">$(\Omega ,\mathcal F,\mathbb P)$</span> a probability space. Let say <span class="math-container">$\Omega =[0,1]$</span>, <span class="math-container">$\mathbb P=m$</span> the lebesgue measure and <span class="math-container"... | https://math.stackexchange.com/questions/2985937/problem-to-understand-random-variable-for-example-x-omega-1-is-really-ra |
Question: <p>I was initially thinking about who would die first, Sean Connery or Roger Moore. Roger Moore passed on later so I got to thinking about could you calculate the odds of one instance versus one single group happening? In my example, what would happen first, an original cast member of the Simpsons dying or Se... | https://math.stackexchange.com/questions/2991957/could-you-calculate-the-odds-of-which-would-happen-first-sean-connery-or-an-ori |
Question: <blockquote>
<p>A machine has <span class="math-container">$5$</span> components and needs at least 3 working components
to function. Suppose that their lifetimes are independent
exponential(1). Find the density function for the time to failure <span class="math-container">$T$</span>.</p>
</blockquote>
<h3>at... | https://math.stackexchange.com/questions/2993505/find-the-density-function-for-the-time-to-failure-t |
Question: <p>How to combine the probability of liking something with the one of it being liked?</p>
<p>I'd like to estimate the probability of a person liking a dish by only having the following two bits of information given:</p>
<ul>
<li>The person likes 70% (<code>like_rate = 0.7</code>) of all dishes you offer him... | https://math.stackexchange.com/questions/2995012/how-to-combine-the-probability-of-liking-something-with-the-one-of-it-being-like |
Question: <p>Suppose that X and Y are integer valued random variables with joint probability mass function given by
<span class="math-container">$p_{X,Y}(a, b)=\begin{cases} \frac{1}{4a}, & 1\leq b\leq a\leq 4\\ 0, & \text{otherwise}. \end{cases}.$</span></p>
<p>(b) Find the marginal probability mass function... | https://math.stackexchange.com/questions/2997775/find-px-y1 |
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