Question

Suppose you just purchased a digital music player and have put 15 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 15 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

15 songs are played.

Answer 1

Answer:

Total songs = 15

Liked songs = 3

Un liked songs = 15-3=12

Find the probability that among the first two songs played

​(a) You like both of them.

Probability that among the first two songs played you like both of them = $\frac{3}{15} \times \frac{2}{14} = 0.029$

​(b) You like neither of them.

Probability that among the first two songs played you like neither of them = $\frac{12}{15} \times \frac{11}{14} = 0.629$

​(c) You like exactly one of them.

Probability that among the first two songs played you like exactly one of them = $\frac{3}{15} \times \frac{12}{14}+ \frac{12}{15} \times \frac{3}{14}= 0.343$

(d) Redo​ (a)-(c) if a song can be replayed before all

​(a) You like both of them. Would this be​ unusual?

Probability that among the first two songs played you like both of them = $\frac{3}{15} \times \frac{3}{15} = 0.04$

​(b) You like neither of them.

Probability that among the first two songs played you like neither of them = $\frac{12}{15} \times \frac{12}{15} = 0.64$

​(c) You like exactly one of them.

Probability that among the first two songs played you like exactly one of them = $\frac{3}{15} \times \frac{12}{15}+ \frac{12}{15} \times \frac{3}{15}= 0.32$