At Thomas Jefferson High School students are heavily involved in extra-curricular activities. Suppose that a student is to be selected at random from this school. Let the events A, M, and S be defined as follows, with the probabilities listed: A = student is active in the performing arts: P(A) = 0.20
M = student is active in vocal or instrumental music: P(M) = 0.32
S = student is active in sports: P(S) = 0.35 P(A intersection M) = 0.18; P(A intersection S) = 0.07; P(M | S) = 0.30
Calculate each of the following (show your work):
a. P(A|M)
b. P(A union M)
c. P(M intersection S)