Suppose a compact disk (CD) you just purchased has 12 tracks. After listening to

Question

Suppose a compact disk (CD) you just purchased has 12 tracks. After listening to the CD you decide that you like 2 of the songs. With the random feature on your CD player, each of the 12 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? You like neither of them. You like exactly one of them. if a song can be replayed before all 12 songs are played. The probability that you like both songs is (Round to three decimal places as needed.)

Explanation / Answer

The number of ways in which the 2 songs can be played from 12 songs = 12C2 = 66

a) Number of ways in which first two can be the ones that are likes = 2 * 1 = 2 ways

Probability = 1/ 66 = 0.01515 which has a low probability of occuring

.

b) To dislike both of them, they must be chosen from 10 of the songs that I dislike

Thus, P (B) = 10C2 / 12C2 = 45 / 66

= 0.6818

.

c)

One has to be chosen from the 2 I like and other has to be chosen from the 10 that I dislike:

P (C) = 2C1 * 10C1 / 12C2 = 0.3030

d)

If songs can be chosen with replacement,

Ways of choosing two songs = 12 * 12 = 144

P(A) = 2 * 2 = 4 ways

= 4 / 144 = 0.027778

P(B) = 10 * 10 = 100 ways

= 100 / 144 = 0.69444

P (C) = (10)(2) + (2)(10) = 40 ways

= 40 / 144 = 0.277778

Hope this helps. Ask if you have doubts.

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