Question

25% of the time there is free breakfast at work. You just woke up and are really hungry, so you call your coworker who is already at work, and he tells you there is free breakfast. However, he lies to you 1/3 of the time. How likely is it that there is free breakfast at work today? *

Answer 1

Answer: P(T|B) = 2/3= 0.667

Explanation:

Given;

Probability that there is free breakfast at work

P(B) = 0.25

Probability that your coworker lied

P(L) = (1/3)

Probability that your coworker did not lie

P(T) = 1-1/3 = 2/3

Since your coworker already told you there is free breakfast, the condition probability now depends solely on whether he lied or not.

P(T|B) = P(B)P(T)/[P(B)P(T) + P(B)P(L)]

P(T|B) = (0.25×2/3)/[(0.25×2/3 + (0.25×1/3)]

P(T|B) = 2/3= 0.667

Hint: since the coworker already confirmed that there is free breakfast, the probability that there will be free breakfast now depends solely on the whether the co-workers said the truth, which have a probability of 2/3.

i.e P(T|B) = P(T) = 2/3