Question

When a child is born, there is a 50% chance it will be a girl.

Suppose a couple would like to have three children.
Determine the theoretical probability of having two girls and one boy.

Answer 1

To find the theoretical probability of having two girls and one boy in a family of three children, with each gender having a 50% chance, we calculate it as 3 x (0.5)^2 x (0.5) = 37.5%.

Step-by-step explanation:

The theoretical probability of having two girls and one boy in a family of three children, given that the probability of having a girl or a boy is 50%, can be calculated using the binomial probability formula. For three children, there are three different sequences in which we could have two girls and one boy (GGB, GBG, BGG). The probability for each of these sequences is (0.5)³ because each child is an independent event.

We have:

• GGB = (0.5)(0.5)(0.5)
• GBG = (0.5)(0.5)(0.5)
• BGG = (0.5)(0.5)(0.5)

Adding up the probabilities for each of these sequences gives us the total probability:

3 x (0.5²) x (0.5) = 3 x (0.25) x (0.5) = 3 x 0.125 = 0.375

So, the theoretical probability of having two girls and one boy is 37.5%.