As in Example 2.27, a student hears ten songs (in a random shuffle mode) and uses F to denote when a song belongs to her favorite type of music, and N for not-favorite, so the sample space consists of all ten-tuples of F's and N's. For each song, the probability that the song is one of her favorite type can be called p, and the probability that the song is not one of her favorite type is 1 - p. Define
A = {(N, N, N, x4,...,xl0) | xj € {F, N}},
B = {(x1F,x3,F,x5,F,x7,F,x9,F) \ xj {F,N}},
C = {{x1,x2,x3,x4,x5,F,F,F,F,F) | xj {F,N}}.
So that, for instance, P(A) = (1 - p)3, and P(B) = P(C) = p5. Find the following conditional probabilities:
P(B | C), P(C | B), P(A | B), P(B | A), P(A | C), P(C | A).