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 four boys in ten births. round the answer to the nearest thousandth

Answer 1

Use the formula for binomial distribution

Answer 2

Answer: 0.205

Explanation:

Binomial probability distribution formula :-

`P(x)=^nC_xp^x(1-p)^(n-x)`, where P(x) is the probability of success in x trials , n is the total number of trials and p is the probability of success.

Given : Male and female births are equally likely, the probability of getting a boy = 0.5

Now, the probability of exactly four boys in ten births :-

`P(x=4)=^(10)C_4(0.5)^4(1-0.5)^(10-4)\\\\=(10!)/(4!6!)(0.5)^4(0.5)^6=0.205078125\approx0.205`

Hence, the probability of exactly four boys in ten births = 0.205