Question

Joe can choose to take the freeway or not for going to work.

There is a 0.4 chance for him to take the freeway. If he chooses freeway, Joe is late to work with probability 0.3; if he avoids the freeway, he is late

with probability 0.1

Given that Joe was early, what is the probability that he took freeway?

Answer 1

A: Event of Joe takes the freeway

: Event of Joe avoids the freeway

B : Event of Joe is early(Not Late) to work

: Event of Joe is late to work

Given,

There is a 0.4 chance for him to take the freeway: P(A) = 0.4;

P() = 1-P(A) = 1-0.4 = 0.6

If he chooses freeway, Joe is late to work with probability 0.3 : P(|A) = 0.3

P(B|A) = 1-P(|A) = 1-0.3=0.7

if he avoids the freeway, he is late with probability 0.1: P(|) = 0.1

P(B|) = 1 - P(|)=1-0.1 = 0.9

Probability that he took freeway Given that Joe was early = P(A|B)

By Bayes Theorem,

Probability that he took freeway Given that Joe was early = 0.341463415