Question

You are a serious student who studies on Friday nights but your roommate goes out and has a good time. 40% of the time he goes out with his girlfriend; 60% of the time he goes to a bar. 30% of the times when he goes out with his girlfriend he spends the night at her apartment. 40% of the times when he goes to a bar he gets in a fight and gets thrown in jail. You wake up on Saturday morning and your roommate is not home. What is the probability that he is in jail?

Answer 1

The probability that your roommate is in jail is 10.8%.

Answer 2

the probability is 0.24 or 24%

Explanation:

Given

Percentage of time he goes out with his girlfriend = 40%

Percentage of time he goes out to a bar = 60%

If he goes out with his girlfriend, the percentage of times he spends the night at his girlfriend’s apartment = 30%

If he goes out to a bar, percentage of times he gets in a fight and gets thrown in jail = 40%

let probability that the roommate went to the bar = A

As the roommate going to jail is a conditional probability dependent on A happening, the true probability of the roommate is found by multiplying the absolute probability of the roommate going out to a bar (A) by the probability of the roommate going to jail if he goes to a bar

that is Pr(B) =Pr (B n A)

Pr(B) = Pr(B/A) *Pr(A)

This is given as 60% * 40% or 0.6 * 0.4 (probabilities are 1/100 of percentages)

This gives an answer of 0.24 or 24%