Probability of two boys and 2 girls?

Question

In a family with 4 children, what is the probability of having 2 boys and then 2 girls, in that order? (Exclude multiple births and assume all outcomes are equally likely).

In a family with 4 children, what is the probability of having 2 boys and 2 girls, in any order? (Exclude multiple births and assume all outcomes are equally likely).

Answer 1

Hi Braeden,

To find the probability of a couple having 2 boys first and then 2 girls is not as complicated as it might seem. First you need to know how many possible orders there are total. For each child, there are two choices: boy (B) or girl (G).

If the couple has four children, then the number of possibilities is 2 x 2 x 2 x 2 = 16. [To use a probability term, the list of possibilities in an experiment is called the sample space. This sample space contains 16 things.]

Only 1 of these orders is BBGG, so the probability is 1/16.

If you are good at systematically listing possibilities (and since there are only 16), you can verify this probability by simply listing everything in the sample space. I will list them below. See if you can see the process I used to list them all. Hint: I typed the first letter of each line first. Then I went back and typed the second letter of each line, then the third letters, and finally the last letters. See a pattern ?? Also, notice that only 1 of these 16 things is BBGG so the probability is 1/16.

BBBB

BBBG

BBGB

BBGG

BGBB

BGBG

BGGB

BGGG

GBBB

GBBG

GBGB

GBGG

GGBB

GGBG

GGGB

GGGG

Hope this helps,

Jim