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 0.198. (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 probability of not - liking a song

The total number of songs is $n = 9$, and the number of liked songs is $4$. So the number of disliked songs is $9 - 4=5$. The probability of not - liking a single song when selection is with replacement is $p=\frac{5}{9}$.

Step2: Calculate probability of not - liking both songs

Since the selections are independent (because a song can be re - played), the probability of not liking both songs is the product of the probabilities of not liking each song. Using the formula for independent events $P(A\cap B)=P(A)\times P(B)$, we have $P=\frac{5}{9}\times\frac{5}{9}=\frac{25}{81}\approx0.309$.

Answer:

$0.309$