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 nine boys in ten births.

Answer 1

Answer: 0.009765625

Explanation:

Binomial probability formula :-

`P(x)=^nC_x\ p^x\ (1-p)^(n-x)`, here P(x) is the probability of getting succeed in x trial, n is the total number of trials and p is the probability of success in each trial.

We 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.

The probability of of getting a boy = The probability of getting a girl = 0.5

Now, the probability of exactly nine boys in ten births will be :-

`P(9)=^(10)C_9\ (0.5)^9\ (0.5)^(1)\\\\=10(0.5)^(10)=0.009765625`

Hence, the probability of exactly nine boys in ten births = 0.009765625