Question

A couple is thinking about having 3 children. Assume that each child is equally likely to be a girl or a boy. What is the probability that exactly 2 of the children are girls?

A. 0.125
B. 0.25
C. 0.375
D. 0.5

Answer 1

O.375

Explanation:

We will start with the second part of the question, listing out all of the possible combinations that can occur from this data set. There is a 50/50 chance of having a girl or a boy, and there are three children. For now we'll use B to represent a boy and G for a girl. It goes as follows:

(B, B, B), (B, B, G), (B, G, B), (B, G, B), (B, G, G), (G, B, B), (G, B, G), (G, G, B), (G, G, G)

I often find it easy to write out a branch diagram to help me visualize this problem and make sure I have all possibilities. (See attached image)

Count the total number of combinations (9). Next, count the number that include exactly 2 girls (4). With this information, we now know that there is a 4 out of 9 chance of having exactly 2 girls and one boy. 4/9 is in simplest form, so all you have to do is find the percentage 44.444%

Answer:

C or 37.5