SOLUTION: The probability that the children of a certain couple will have red hair is 0.223. If the couple were to have five children, what is the probability that exactly two of them will h

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Question 601029: The probability that the children of a certain couple will have red hair is 0.223. If the couple were to have five children, what is the probability that exactly two of them will have red hair?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
P(X = x) = (n C x)*(p)^(x)*(1-p)^(n-x)

P(X = 2) = (5 C 2)*(0.223)^(2)*(1-0.223)^(5-2)

P(X = 2) = (5 C 2)*(0.223)^(2)*(0.777)^(5-2)

P(X = 2) = (10)*(0.223)^(2)*(0.777)^3

P(X = 2) = (10)*(0.049729)*(0.469097433)

P(X = 2) = 0.23327746245657


So the probability that exactly two of them will have red hair is approximately 0.233277