Question 601029
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