standard_description: Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. For example, find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiple-choice test where each question has four choices, and find the expected grade under various grading schemes.
problem_activity: Problem 1
At a particular diner, everyone drinks coffee. However, some people drink their coffee with sugar, some with cream, some with both, and some with neither.
Describe the coffee preferences of the 30 people in the diner in the Venn diagram below. Be sure to label the circles appropriately.
10 people just like cream in their coffee.
13 people like sugar in their coffee; 8 of these people also like cream.
7 people like neither cream nor sugar in their coffee.
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Problem 2
Below is a diagram that shows all of the members of the student council at a particular high school. Each member is represented by a labeled point. The students that are in circle “
$$J$$
” are juniors and the students in circle “
$$M$$
” are male.
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Find
$$P(J)$$
.
Find
$$P(M)$$
.
Find
$$P(J \space and \space M)$$
.
Find
$$P(J \space or \space M)$$
.
Why does
$$ P(J \space or \space M)≠P(J)+P(M)$$
? Design a formula to calculate
$$P(J \space or \space M)$$
using any of the probability found in (a) through (c).


aligns: no