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 = $\frac{3}{15} \times \frac{12}{15}+ \frac{12}{15} \times \frac{3}{15}= 0.32$

Answer 2

This is about probability and combinations.

a) 0.0286

b) 0.6286

c) 0.3429

d) 0.04, 0.64, 0.32

• Total number of songs in music player = 15 tracks

• Number of songs you like = 3 songs

• Number of songs you don't like = 15 - 3 = 12

• A) Probability you will like the first one = 3/15

After the first one, there are 14 left and 2 you may like. Probability you will like the second one = 2/14. Thus;

P(you like both of the first two played) = 3/15 × 2/14

P(you like both of the first two played) = 0.0286

• B) Probability you will not like the first one = 12/15

After the first one, there are 14 left and 11 you may not like. Probability you will not like the second one = 11/14. Thus;

P(you like both of the first two played) = 12/15 × 11/14

P(you like neither of the first two played) = 0.6286

• C) Probability you like exactly one of them means you may like the first and dislike the second or you may dislike the first and like the second. Thus, this probability is;

P(like exactly one of the first two) = (3/15 × 12/14) + (12/15 × 3/14)

P(like exactly one of the first two) = 0.3429

• d) If a song is replayed before all, then;

a) P(you like neither of the first two played) = 3/15 × 3/15

P(you like neither of the first two played) = 0.04

b) P(you like neither of the first two played) = 12/15 × 12/15

P(you like neither of the first two played) = 0.64

c) P(like exactly one of the first two) = (3/15 × 12/15) + (12/15 × 3/15)

P(like exactly one of the first two) = 0.32

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