Question

In a certain​ country, the true probability of a baby being a girl is 0.469. Among the next seven randomly selected births in the​ country, what is the probability that at least one of them is a boy​?

Answer 1

The probability is 0.995 ( approx ).

Explanation:

Let X represents the event of baby girl,

The probability of a baby being a girl is, p = 0.469,

So, the probability of a baby who is not a girl is, q = 1 - 0.469 = 0.531,

Also, the total number of experiment, n = 7

Thus, by the binomial distribution formula,

`P(x)=^nC_x(p)^x q^(n-x)`

Where,
`^nC_x=(n!)/(x!(n-x)!)`

The probability that all babies are girl or there is no baby boy,

`P(X=7)=^7C_7(0.469)^7(0.531)^(7-7)`

`=0.00499125661758`

Hence, the probability that at least one of them is a boy​ = 1 - P(X=7)

= 1 - 0.00499125661758

= 0.995008743382

≈ 0.995