What is the probability of getting 2 girls and 2 boys of 4 children?

Answer 1

It depends. If the order is important, (2 girls then 2 boys): There's a 1/2 chance of any sex, so the probability is 1/16(or 6.25%). But if it's just any order of 2 girls and 2 boys, then it's a different outcome. Consider the following table. The desired outcome is 2 girls, 2 boys in any order. We can just look for 2 girls, and convert to Boolean values of 1 for girl and 0 for boy. Here is the table:

0 0 0 0: 0

0 0 0 1: 1

0 0 1 0: 1

0 0 1 1: 2*

0 1 0 0: 1

0 1 0 1: 2*

0 1 1 0: 2*

0 1 1 1: 3

1 0 0 0: 1

1 0 0 1: 2*

1 0 1 0: 2*

1 0 1 1: 3

1 1 0 0: 2*

1 1 0 1: 3

1 1 1 0: 3

1 1 1 1: 4

Note each row has five numbers. The first four numbers represent the four children, and the fifth number is a sum of these four numbers. Any time the sum equals exactly 2, then the desired outcome (2 out of the four children are girls).

This happens 6 times out of the 16 total possible outcomes, so the probability is 6/16, or 3/8 = 37.5%