Question

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.)

A. 279/8000
B. 2187/8000
C. 729/2000
D. 9/10

Answer 1

There are 3 ways to get 2 female and 1 male singer.
These 3 ways are
FFM, FMF and MFF
Each of the three ways has probability 45% * 45% * 45% = 9.1125%
As there are three ways multiply by 3
= 27.3375%
hope it helps