What percentage of families with five children can we expect

What percentage of families with five children can we expect to have three girls and two boys?

Solution

For this question, we will apply probability rule called COMBINATION(C) ,

For each of the 5 children, there are 2 possibilities - boy or girl - thus 2^5 possibilities
one of the \"favourable\" ones is GGGBB, but the 3 girls could be anywhere in the sequence, in 5c3 = 10 ways
thus Probability = 10/2^5 = 5/16, ie 31.25% .