Question

Mr. Brown's statistics class consists of 21 seniors. The class took two quizzes in one week, and 12 of the students in the class passed both quizzes. What is the probability that the same students who passed the first quiz also passed the second quiz given that 19 students passed the first quiz?A. P(S/F) = 0.63B. P(S/F) = 0.2 C. P(S/F) = 0.8 D. P(S/F) = 1.31

Answer 1

This is a case of conditional probability. The conditional probability of an event, A given that B has occured is is written as P(AIB). We would caluculate the probability as

P(AIB) = Probability of A and B)/Prrobability of B

Looking at the iven question, Probability of S and F is 12/21 (12 of the students in the class passed both quizzes)

Probability of S = 19/21

Therefore,

P(SIF) = (12/21) / (19/21)

(PSIF) = 12/21 * 21/19

(PSIF) = 12/19 = 0.63

The correct option is A