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.
a. The probability is
(Simplify your answer.)