Question

Suppose you just purchased a digital music player and have put 8 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 8 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.

Answer 1

Answer:

a) 21.43% (It is unusual to happen)

b) 21.43%

c) 57.14%

d) Probability of you liking both songs played = 25%

Probability of liking exactly one song = 50%

Step-by-step explanation:

a)

If you like 4 of the 8 songs, the probability of liking the first song is 4/8

Then, for the second song, we have 3 songs you like among 7 songs that can be played, so the probability is 3/7.

So the probability of you liking both songs played is:

P = (4/8) * (3/7) = 0.2143 = 21.43% (It is unusual to happen)

b)

If you like 4 of the 8 songs, you dislike 4 as well, so the probability of not liking the first song is 4/8.

Then, for the second song, we have 3 songs you dislike among 7 songs that can be played, so the probability is 3/7.

So the probability of you disliking both songs played is:

P = (4/8) * (3/7) = 0.2143 = 21.43%

c)

In this case you can like either the first or the second song, so we need to sum the probabilities of both cases:

Probability of liking the first song and disliking the second:

P1 = (4/8) * (4/7) = 0.2857

Probability of disliking the first song and liking the second:

P2 = (4/8) * (4/7) = 0.2857

P = P1 + P2 = 0.5714 = 57.14%

d)

If a song can be replayed, we have:

Probability of you liking both songs played:

P = (4/8) * (4/8) = 0.25 = 25%

Probability of liking the first song and disliking the second:

P1 = (4/8) * (4/8) = 0.25

Probability of disliking the first song and liking the second:

P2 = (4/8) * (4/8) = 0.25

P = P1 + P2 = 0.5 = 50%