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 honor 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?

Question

Mathematics

Isabela

1 January, 19:22

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 honor 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?

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Answers (1)

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India Stewart · Answer 1

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%

Final Answer: 37%