Question

Suppose you just purchased a digital music player and have put 12 tracks on it. After listening to them you decide that you like 2 of the songs. With the random feature on your​ player, each of the 12 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 12 songs are played.

Answer 1

The answer is below

Explanation:

We have the following information:

Number of songs you like = 2

Total number of songs = 12

a) P(you like both of them) = 2/12 x 1/11 = 0.015

This is unusual because the probability of the event is less than 0.05

b) P(you like neither of them) = 10/12 x 9/11 = 0.68

c) P(you like exactly one of them) = 2 x 2/12 x 10/11 = 0.30

d) If a song can be replayed before all 12,

P(you like both of them) = 2/12 x 2/12 =0.027

This is unusual because the probability of the event is less than 0.05

P(you like neither of them) = 9/12 x 9/12 = 0.5625

P(you like exactly one of them) = 2 x 2/12 x 9/12 = 0.25