MATH SOLVE

5 months ago

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]