Question

suppose you just purchased a digital music player and have put 9 tracks on it. after listening to them you decide that you like 4 of the songs. with the random feature on your player, each of the 9 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 9 songs are played. (b) the probability that you like neither song is 0.278 (round to three decimal places as needed.) (c) the probability that you like exactly one song is 0.556 (round to three decimal places as needed.) (d) the probability that you like both songs is (round to three decimal places as needed.)

Explanation:

Step1: Calculate probability when songs can be re - played

The probability of liking a song is $p=\frac{4}{9}\approx0.444$ and the probability of not liking a song is $q = 1 - p=1-\frac{4}{9}=\frac{5}{9}\approx0.556$.

Step2: Probability of liking both songs

For independent events (since a song can be re - played), we use the multiplication rule for independent events. The probability of liking the first song and liking the second song is $P(\text{like both})=p\times p$.
$P(\text{like both})=\frac{4}{9}\times\frac{4}{9}=\frac{16}{81}\approx0.198$

Answer:

0.198