Question

Assume that male and female births are equally likely and that the birth of any child does not affect the probability of the gender of any other children. Find the probability of exactly five girls in ten births.

Please show your work! Thanks!

Answer 1

The probability is 0.2461

or 24.6% to the nearest tenth.

Explanation:

This is a Binomial Probability Distribution.

The formula for B(r; n,p) = nCr p^r (1 - p)^(n-r) where r = number of successes, p = probability of a success.

Here, r = 5 , n = 10 and p = 1/2.

So for 5 girls in 10 births it is

10C5 (1/2)^5 (1 - 1/2)^(10-5)

= 252 * 1/32 * 1/32

= 0.2461.