Question

, 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.)

Answer 1

Answer is
P=P(FFM)+P(FMF)+P(MFF)
Assuming a large population (meaning that the probabilities do not change after choosing a song), then P(F)=P(M)=0.45, and assuming independence among choices, then
\[P(FFM)=0.45^2*0.45=0.45^3\]
But P(FFM)=P(FMF)=P(MFF), therefore P=3P(FFM)