Suppose you just purchased a digital music player and have put 14 tracks on it.

Question

Suppose you just purchased a digital music player and have put 14 tracks on it. After listening to them you decide that you like 4 of the songs. With the random feature on your player, each of the 14 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 8 songs are played.

(a) The probability that you like both songs is ___ (Round to three decimal places as needed)

Would this be unusual for you to like both songs Yes or No

(b) The probability that you like neither songs is ___ (Round to three decimal places as needed)

(c) The probability that you like exactly one song is ___ (Round to three decimal places as needed)

(d) redo (a)-(c) if a song can be replayed before all 14 songs are played.

The probability that you like both songs is ___ (Round to three decimal places as needed)

The probability that you like neither songs is ___ (Round to three decimal places as needed)

The probability that you like exactly one song is ___ (Round to three decimal places as needed)

Explanation / Answer

The number of ways of selecting 2 songs randomly from 14 is 14C2=(14*13)/2=91.

Number of ways of selecting 2 songs from 4 liked songs is 4C2 = (4*3)/2 = 6.

(a) Probability that i like both songs = (4C2)/(14C2) = 6/91 = 0.066

(b) Probability that I like neither of the songs = (10C2)/(14C2) = 45/61 = 0.738

(c) Probability that I like exactly one song = (10C1)*(4C1)/(14C2) = (10*4)/61 = 40/61 = 0.656

(d)(1) Probability that I like both songs = (4*4)/(14*14) = 0.082

(2) probability that I like neither of both = (10*10)/(14*14) = 0.510

(3) Probability that I like exactly one song = (10*4)/(14*14) = 0.204

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