Let NT denote the event that a randomly selected listener is not tired of the song. Because we estimate that P(T) = .17 and P(T 11) = .70, we estimate that
P(NT) = 1 - P(T) = .83 and P(NT | 1) = 1 - P(T | 1) = .30
a. Estimate P(NT | 5), P(NT | 4), P(NT | 3), and P(NT | 2).
b. Estimate P(5 |NT), P(4 |NT), P(3 |NT), P(2 |NT), and P(1 |NT).
c. The reason that the probabilities in b do not sum to 1(with rounding) is that, if a listener is not tired of the song, the listener could be unfamiliar (UNFAM) with the song, Using the facts that
P(UNFAM) = 1 - P(FAM) = .09 and P(NT | UNFAM) = 1
Find P(UNFAM ( NT), P(UFAM | NT), and P(UNFAM ( NT).