Question

In a certain​ country, the true probability of a baby being a

girl

is

0.461

Among the next

four

randomly selected births in the​ country, what is the probability that at least one of them is a

boy​?

The probability is.

Answer 1

G : Event of a baby being a girl

P(G) = 0.461

Number of randomly selected births = 4

Probability that at least one of them is a boy​ = 1 - Probability that none of them is boy

Probability that none of them is boy = Probability that all of them are girls

Probability that all of them are girls when 4 births are selected

= Probability that first selected birth is a girl x Probability that second birth is a girl x Probability that third birth is a girl x Probability that fourth birth is a girl

= P(G) x P(G) x P(G) x P(G) = 0.461 x 0.461 x 0.461 x 0.461 = 0.045165175

Probability that none of them is boy = Probability that all of them are girls =  0.045165175

Probability that at least one of them is a boy​ = 1 - Probability that none of them is boy = 1 - 0.045165175= 0.954834825

Among the next four randomly selected births, Probability that at least one of them is a boy​ = 0.954834825

The probability is 0.954834825