At a certain university, 30% of the students who take basic statistics are firstyear students, 35% are sophomores, 20% are juniors, and 15% are seniors.
From records of the statistics department it is found that out of the first-year students who take the basic statistics course 20% get As; out of the sophomores who take the course 30% get As; out of the juniors 35% get As; and out of the seniors who take the course 40% get As.
Given that a student got an A in basic statistics, what is the probability that she or he is a senior?