In this exercise we estimate the proportions of listeners familiar with the song who would give the song each rating. Using the definition of conditional probability, we estimate that

Note here that P(5 ( FAM) equals P(5) because the event 5 ( FAM and the event 5 are equivalent. That is, a randomly selected listener would give the song a rating of 5 if and only if the listener is familiar with the song and would give the song a rating of 5. By using similar reasoning, find P(4 | FAM), P(3 | FAM), P(2 | FAM), and P(l | FAM).

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P(5 n FAM) P(5)18 P(FAM) PFAM) 91 Pl5l FAM) =-= .1978