College admissions Suppose that you have applied to two colleges and believe that you have a 0.80 probability of being accepted by college A, a 0.40 probability of being accepted by college B, and a 0.35 probability of being accepted by both. You will investigate how the probability that you will be accepted by one of these colleges changes if you find out whether you have been accepted by the other. Start by converting the given probabilities into a 2 2 table of counts to help make things more concrete. Let's assume that these probabilities held exactly for a hypothetical population of 1,000 applicants. Notice that the counts provided in the following table correspond to the given 0.80, 0.40, and 0.35 probabilities. Fill in the missing counts in the table. Accepted by B Not accepted by B Total Accepted by A 350 800 Not accepted by A Total 400 1000