in a city school of 1,200 students, 40% of the students are on the honor roll, 60% have a part-time job, and 22% are on the hono
r roll and have a part-time job. What is the probability (rounded to the nearest whole percent) that a randomly selected student is on the honor roll, given that the student has a part-time job?
Let A = event that the student is on the honor roll B = event that the student has a part-time job C = event that the student is on the honor roll and has a part-time job
We are given P(A) = 0.40 P(B) = 0.60 P(C) = 0.22 note: P(C) = P(A and B)
We want to find out P(A|B) which is "the probability of getting event A given that we know event B is true". This is a conditional probability
P(A|B) = [P(A and B)]/P(B) P(A|B) = P(C)/P(B) P(A|B) = 0.22/0.6 P(A|B) = 0.3667 which is approximate
Convert this to a percentage to get roughly 36.67% and this rounds to 37%
