The probability of having a boy is 0.51. What is the probability that there are 3 boys in a family with five children?

The probability of having a boy is p = 0.51;
The probability that a boy is not born: q = 1 – p = 1 – 0.51 = 0.49.
Using the Bernoulli formula, we determine the probability that out of 5 children, three will be boys:
P5 (3) = C (5,3) p ^ 3 q ^ 2;
C (5,3) = 5! / (3! 2!) = 4 5/2 = 10;
P5 (3) = 10 0.51 ^ 3 0.49 ^ 2 = 0.318.
Answer: The probability that there are three boys out of 5 children is 0.318.