Solution(s): {(3, 6), (6, 3), (4, 5), (5, 4)} What is the probability that the sum of two die rolled will be 9? Comment(s): Students should remember that probabilities are the number of desired outcomes divided by the size of the sample space. These terms should be reviewed. Solution(s): 4/36 = 1/9 Using your lattice, determine the probability of having at least one of the two dice show an odd number. Comment(s): Students may simply get this incorrect by miscounting to 27. Solution(s): 27/36 = 3/4 The different outcomes that determine the probability of rolling odd can be visualized using a Venn Diagram, the beginning of which is seen below. Each circle represents the possible ways that each die can land on an odd number. Circle A is for the first die landing on an odd number and circle B for the second die landing on odd. The circles overlap because some rolls of the two dice are successes for both dice. In each circle, the overlap, and the area outside the circles, one of the ordered pairs from the lattice has been placed. appears in circle A because the first die is odd, appears in circle B because the second die is odd, appears in both circles at the same time (the overlap) because each die is odd, andappears outside of the circles because neither dice is odd. Finish the Venn Diagram by placing the remaining 32 ordered pairs from the dice lattice in the appropriate place.
Find . What is another way to write the probability of using a complement? Find . Find . The Conditions are Right MCC9-12.S.CP.2 Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. ★ MCC9-12.S.CP.3 Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B. ★ MCC9-12.S.CP.4 Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. ★ MCC9-12.S.CP.5 Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. ★ MCC9-12.S.CP.6 Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model. ★ Imagine the last time you entered to win a raffle at a fair or carnival. You look at your ticket, 562104. As they begin to call off the winning ticket, you hear 562, but everyone has the same first 3 digits. Then 1 and 0 are called off. You know that excited feeling you get? Did you know there is a lot of math behind that instinct you feel that you might just win the prize? Now imagine those times when you are waiting to get your latest grade back on your English test. You’re really not sure how you did, but as your teacher starts to talk about test results, her body
Find the probability that a given cancer-free person was not a smoker and represent it with proper notation. How does the probability in number 6 compare to ? Are they the same or different and how so? Based upon finding the conditional probabilities make an argument that supports the connection between smoking and lung cancer. Part 3 – A Formula for Conditional Probability The formulaic definition of conditional probability can be seen by looking at the different probabilities you calculated in part 2. The formal definition for the probability of event A given event B is the chance of both events occurring together with respect to the chance that B occurs. As a formula, Probability of A given B In part 2 you found that and. Using the formula for conditional probability is another way to determine that: Using the same approach that is shown above, show that the conditional probability formula works for . For two events S and Q it is known that and. Find . For two events X and Y it is known that and. Find . For two events B and C it is known that and. Find . For two events V and W it is known that and. Find. For two events G and H it is known that and. Explain why you cannot determine the value of.