Question

What is the probability of having 3 boys in a family of 3 boys?

Answer 1

The probability of having 3 boys in a family of 3 children can be calculated using the concept of binomial probability.

Step-by-step explanation:

The probability of having 3 boys in a family of 3 children can be calculated using the concept of binomial probability.

1. First, we need to determine the probability of having a boy or a girl in each birth. Since there are two possible outcomes (boy or girl), the probability of having a boy is 1/2 (0.5) and the probability of having a girl is also 1/2 (0.5).
2. Next, we use the binomial probability formula:

P(x = k) = C(n, k) * p^k * (1-p)^(n-k)

1. In this case, n = 3 (number of children) and k = 3 (number of boys). Therefore, the probability can be calculated as:

P(x = 3) = C(3, 3) * (0.5)^3 * (1-0.5)^(3-3) = 1 * 0.125 * 1 = 0.125

So, the probability of having 3 boys in a family of 3 children is 0.125 or 12.5%.