A Nashville-area radio station plays songs from a specific, fixed set of artists. The station has no DJ; instead, a computer randomly selects which songs to play. The songs themselves are picked randomly, and the same song may be played many times in a row. In the set of songs, 45% are sung by a female singer, 45% are sung by a male singer, and 10% are instrumental with no vocals. What is the probability that a particular set of 3 songs contains exactly 2 female singers and 1 male singer? (Hint: Be aware that there are multiple ways to achieve this pattern of songs.)

Question

Emmanuel Obrien

Mathematics

5 April, 06:03

A Nashville-area radio station plays songs from a specific, fixed set of artists. The station has no DJ; instead, a computer randomly selects which songs to play. The songs themselves are picked randomly, and the same song may be played many times in a row. In the set of songs, 45% are sung by a female singer, 45% are sung by a male singer, and 10% are instrumental with no vocals. What is the probability that a particular set of 3 songs contains exactly 2 female singers and 1 male singer? (Hint: Be aware that there are multiple ways to achieve this pattern of songs.)

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Answers (1)

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Christine Yu · Answer 1

The answer is 27.3375%.

To calculate this, a multiplication rule is used. The multiplication rule calculates the probability that both of two events will occur. In this method, the possibilities of each event are multiplied.

So, we have three events occurring simultaneously:

1. set contains female singer: 45% = 0.45

2. set contains female singer: 45% = 0.45

3. set contains female singer: 45% = 0.45

Also, it should be taken into consideration that there are three set combinations:

female-female-male,

female-male-female,

male-female-female

So, the probability for one set of the song is:

0.45 * 0.45 * 0.45 = 0.091125

Therefore, the probability is multiple ways to achieve this pattern of songs):

3 * 0.091125 = 0.273375 = 27.3375%.