Question

In a certain country, the true probability of a baby being a boy is 0.538. Among the next four randomly selected births in the country, what is the probability that at least one of

them is a girl?
The probability is

Answer 1

0.916

Explanation:

In a certain country, the true probability of a baby being a boy is p = 0.538, then the true probability of a baby being a girl is q = 1 - 0.538 = 0.462.

Among the next four randomly selected births in the country, the probability that at least one of them is a girl is

`P=C^4_1p^(4-1)q^1+C^4_2p^(4-2)q^2+C^4_3p^(4-3)q^3+C^4_4p^(4-4)q^4`

or

`P=1-C^4_0p^(4-0)q^0=1-(4!)/(0!(4-0)!)p^4=1-(4!)/(4!)(0.538)^4=1-(0.538)^4\approx 0.916`