Question

In the united states, the true probability of a baby being a boy is 0.512 (based on the data available at this writing). among the next five randomly selected births in the united states, what is the probability that at least one of them is a girl?

Answer 1

The probability of at least one girl is the complement of probability of none girl.
i.e.
Probability of at least 1 girl = 1 - Probability of none girl

Probability of none girl means all 5 baby boys are born. So first we find the probability of all 5 babies being born as boys.

Probability of being a boy = 0.512
Since the birth of next baby is independent of the previous ones, we can write:

Probability of 5 baby boys =
`(0.512)^(5)`
So,
Probability of no baby girl =
`(0.512)^(5)`

Thus,
Probability of at least one baby girl = 1 -
`(0.512)^(5)` = 0.945

The final answer is rounded of to three decimal digits.