Suppose you just purchased a digital music player and have tracks on it. After l

Question

Suppose you just purchased a digital music player and have tracks on it. After listening to them you decide that you like 3 of the songs. With the random feature on your player, each of the 9 songs is played once in random order. Find the probability that among the first two songs played (a) You like both of them. Would this be unusual? (b) You like neither of them. (c) You like exactly one of them. (d) Redo (a)-(c) if a song can be replayed before all 9 songs are played. (a) The probability that you like both songs is (Round to three decimal places as needed.)

Explanation / Answer

a) P (like both song) = 3C2 / 9C2

= 3/36 = 1/12 = 0.083

0.08 > 0.05, so this would not be unusual.

B) P (like neither of them) = 6C2 / 9C2 = 15/36 = 0.417. C) P(exactly one of them) =( 3C1 * 6C1) / 9C2

= 18/36 = 1/2 = 0.5

D) p(like both song) = 3/9 * 3/9 = 9/81 = 1/9 = 0.111

0.111 > 0.05, so it would not be unusual.

P( like neither of them) = 6/9 * 6/9 = 4/9 = 0.444

P(like exactly one of them) = 3/9 * 6/9 + 6/9 * 3/9

= 2/9 + 2/9 = 4/9 = 0.444

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