Suppose you just purchased a digital music player and have put 9 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 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) consider the first song played. The probability of its being liked is 4/9.

And for second song, we have 3 liked songs and 8 remaining songs.

Hence probability of second being liked is 3/8.

Overall probability = (4/9) * (3/8) = 1/6 = 0.167 hence it is almost unusual.

b) First song being not liked is 5/9.

And for second song being not liked is 4/8.

Hence overall probability = (5/9) * (4/8) = 5/18.

c) To like exactly one of them, it has 2 possibilities. First song may be liked and second song disliked = (4/9) * (5/8) = (5/18)

First song may be disliked and second song liked = (5/9) * (4/8) = (5/18)

Hence overall probability = (5/18) + (5/18) = 5/9

d) a) Probability of 2 songs liked by me with replacement means in both cases i have to select a song from 4 liked songs.

Hence probability = (4/9) * (4/9) = 16/81

b) probability of both being not liked by me is = (5/9) * (5/9) = (25/81)

c) probability of exactly one being liked = (4/9) * (5/9) + (5/9) * (4/9) = 40/81