Question

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.)

Answer 1

Answer:

C  (81/500)

Step-by-step explanation:

Answer 2

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