A Dallas-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, 40% are sung by a male singer, and 15% are instrumental with no vocals. What is the probability that a particular set of three songs contains one male singer, one female singer, and one instrumental? (Hint: Be aware that there are multiple ways to achieve this pattern of songs.)

Question

Mathematics

Keegan James

14 May, 23:47

A Dallas-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, 40% are sung by a male singer, and 15% are instrumental with no vocals. What is the probability that a particular set of three songs contains one male singer, one female singer, and one instrumental? (Hint: Be aware that there are multiple ways to achieve this pattern of songs.)

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Answers (1)

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Tyson Hunter · Answer 1

There are three ways to achieve the combination of one male singer, one female singer, and no voice instrumental

Male - Female - No Voice

Male - No Voice - Female

Female - Male - No Voice

Female - No Voice - Male

No Voice - Male - Female

No Voice - Female - Male

For each combination, the probabilities are

MFN = 0.45*0.4*0.15 = 0.027

MNF = 0.45*0.15*0.4 = 0.027

FMN = 0.4*0.45*0.15 = 0.027

FNM = 0.4*0.15*0.45 = 0.027

NFM = 0.15*0.4*0.45 = 0.027

NMF = 0.15*0.45*0.4 = 0.027

Then add all the probabilities we have 0.027*6 = 0.162