At a​ fundraiser, a participant is asked to guess what is inside an unlabeled can for a possible prize. If there are two crates of cans to choose​ from, each having a mixture of vegetables and​ soup, what is the probability that the selected can came from the left crate given that it is a vegetable can in the following​ situations? a. The left crate has 2 cans of vegetables and​ 8 cans of​ soup, and the right crate has 7 cans of vegetables and 3 cans of soup.
b. The left crate has 8 cans of vegetables and​ 2 cans of​ soup, and the right crate has 5 cans of vegetables and 5 cans of soup.