Question

suppose that a spotify playlist has 8 tracks. after listening to all the songs, you decide that you like 3 of them. with the random feature on the playlist, each of the 8 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 8 songs are played (if, for example, track 2 can play twice in a row). would it be unusual for you to like both of the songs? choose the correct answer no yes (b) the probability that you like neither song is 0.357 (round to three decimal places as needed.) (c) the probability that you like exactly one song is 0.536 (round to three decimal places as needed.) (d) the probability that you like both songs is 0.141 (round to three decimal places as needed.) the probability that you like neither song is (round to three decimal places as needed.)

Explanation:

Step1: Calculate the probability of liking neither song (with replacement)

The probability of not liking a song is \(P(\text{not like})=\frac{8 - 3}{8}=\frac{5}{8}\)
Since the selections are independent (with replacement), we use the multiplication rule for independent events.
The probability that you like neither of the two songs is \(P=\frac{5}{8}\times\frac{5}{8}\)

$$P=\frac{25}{64}\approx0.391$$

Answer:

\(0.391\)