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?
A. 729/8,000
B. 2,187/8,000
C. 729/2,000
D. 9/10

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?
A. 729/8,000
B. 2,187/8,000
C. 729/2,000
D. 9/10

anonymous · Answer

Someone should help me on this, please.. :(

anonymous · Answer

Brute force: FFM+FMF+MFF = 3(0.45)(0.45)(0.45) = 0.273

That is B, if you calculate it.