Question

Let B represent the number of students played basketball and F represent the number of students played football.

a. Find PBF (∪)

Answer 1

The questions are about finding the probability of combined events. Independent events like A and B have their probabilities multiplied to find P(A AND B), while for dependent events, the formula P(B AND D) = P(D|B) * P(B) is used.

Step-by-step explanation:

The student is asking about the probability of combined events, specifically the probability of two events occurring simultaneously (denoted as P(A AND B)) or the probability of one event given that another has occurred (denoted as P(B|A)).

For question 60, where events A and B are independent, the probability of both events A and B occurring is calculated by multiplying their individual probabilities: P(A AND B) = P(A) * P(B) = 0.3 * 0.5 = 0.15.

In the 'Try it' example, to find P(B AND D), where D occurs given that B occurred, we use the formula: P(B AND D) = P(D|B) * P(B) = 0.5 * 0.40 = 0.20.