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. (a) the probability that you like both songs is \\(\square\\) (round to three decimal places as needed.)

Explanation:

Step1: Calculate probability of liking first song

The probability of liking the first - song is the number of liked songs divided by the total number of songs. There are 4 liked songs out of 9, so the probability $P_1=\frac{4}{9}$.

Step2: Calculate probability of liking second song given first is liked

After playing the first liked song, there are 3 liked songs left out of 8 remaining songs. So the probability of liking the second song given the first is liked is $P_2=\frac{3}{8}$.

Step3: Calculate probability of liking both songs

By the multiplication rule for dependent events, the probability of liking both songs is $P = P_1\times P_2=\frac{4}{9}\times\frac{3}{8}=\frac{12}{72}=\frac{1}{6}\approx0.167$.

Answer:

$0.167$