Q:

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 all15 songs are played.

Accepted Solution

A:
Answer:Total songs = 15Liked songs = 3Un liked songs = 15-3=12Find 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 = [tex]\frac{3}{15} \times \frac{2}{14} = 0.029[/tex]​(b) You like neither of them.Probability that among the first two songs played you like neither of them = [tex]\frac{12}{15} \times \frac{11}{14} = 0.629[/tex]​(c) You like exactly one of them.Probability that among the first two songs played you like exactly one of them = [tex]\frac{3}{15} \times \frac{12}{14}+ \frac{12}{15} \times \frac{3}{14}= 0.343[/tex](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 = [tex]\frac{3}{15} \times \frac{3}{15} = 0.04[/tex]​(b) You like neither of them.Probability that among the first two songs played you like neither of them = [tex]\frac{12}{15} \times \frac{12}{15} = 0.64[/tex]​(c) You like exactly one of them.Probability that among the first two songs played you like exactly one of them = [tex]\frac{3}{15} \times \frac{12}{15}+ \frac{12}{15} \times \frac{3}{15}= 0.32[/tex]