What is the probability that it takes Alice more than 37 minutes to finish making dinner given that it has already taken her more than 31 minutes in the making of her dinner?

Question

The amount of time it takes Alice to make dinner is continuous and uniformly distributed between 13 minutes and 40minutes. What is the probability that it takes Alice more than 37 minutes to finish making dinner given that it has already taken her more than 31 minutes in the making of her dinner?

Answer 1

We are reduced to the part of the uniform distribution between 31 and 40. We are interested in the probability of her time being between 37 and 40. That would be (40 - 37) / (40-31) = 1/3