Suppose you just purchased a digital music player and have put 14 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 14 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 14 songs are played.
(a) The probablility that you like both songs is (Round to three decimal places as needed.)
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- Summer 2023) is based on Sullivan: Statistics: Informed Decisions Using Data, $6 e$

Step 1 ：The problem is asking for the probability of certain events happening when songs are played randomly on a music player. The total number of songs is 14, and the number of liked songs is 3.

Step 2 ：For part (a), we need to find the probability that both of the first two songs played are liked. This is a combination problem, where we are choosing 2 liked songs out of 3, and the total number of possible outcomes is choosing 2 songs out of 14.

Step 3 ：The formula for combinations is \(C(n, k) = \frac{n!}{k!(n-k)!}\), where n is the total number of items, k is the number of items to choose, and '!' denotes factorial.

Step 4 ：Let's calculate this probability.

Step 5 ：n = 14

Step 6 ：k = 3

Step 7 ：liked_songs_combinations = 3

Step 8 ：total_combinations = 91

Step 9 ：probability = 0.03296703296703297

Step 10 ：The probability that both of the first two songs played are liked is approximately 0.033. This is a relatively low probability, so it would be considered unusual for this to happen.

Step 11 ：Final Answer: The probability that you like both of the first two songs played is approximately \(\boxed{0.033}\). This would be considered unusual.