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A particular iPod playlist contains 100 songs, 10 of which are by the Beatles. Suppose the shuffle feature is used to play the songs in random order with no repeating. What is the probability that the first Beatles song heard is the fifth song played? What is the probability that there are exactly two Beatles songs in the first five songs played?

Question

A particular iPod playlist contains 100 songs, 10 of which are by the Beatles. Suppose the shuffle feature is used to play the songs in random order with no repeating. What is the probability that the first Beatles song heard is the fifth song played? What is the probability that there are exactly two Beatles songs in the first five songs played?

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Step 1

It is given that the total number of songs is 100 of which 10 are by the Beatles. Therefore, probability of getting Beatle song is 0.10. The selection of songs are the Bernoulli trials with probability 0.10. The geometric distribution gives the probability of number of failures before getting first success for the series of Bernoulli trials.

The probability mass function of geometric distribution is given below.

P(Xx) x= 0,1,2,
0
Otherwise
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P(Xx) x= 0,1,2, 0 Otherwise

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Step 2

The probability that the first Beatle song heard is th...

P(X 4)(0.9) (0.1)
0.06561
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P(X 4)(0.9) (0.1) 0.06561

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