Question

On average, a proportion of 0.48 newborns are girls. What are the chances that in a family with 4 children there are exactly three daughters.

Give your answer as a proportion, rounding to two decimal places.

Answer 1

This is a binomial probability problem.

The probability that in N trials, there will be

exactly x succesful outcomes, if the probability

of a success in 1 trial is p, is given by the

formula

NCx%2Ap%5Ex%2A%281-p%29%5E%28N-x%29

We seek the probability that in 4 trials, there

will be exactly 4 succesful outcomes (girls),

given that the probability of a success (girl)

in 1 trial is 0.48,

4C3%2A%280.48%29%5E3%2A%281-0.48%29%5E%284-3%29

4%2A%280.110592%29%2A%280.52%29%5E1

4%2A%280.110592%29%2A%280.52%29

0.23003136

Round to 0.23, write as 23%2F100