Answer:
0.916
Step-by-step 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
[tex]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[/tex]
or
[tex]P=1-C^4_0p^{4-0}q^0=1-\dfrac{4!}{0!(4-0)!}p^4=1-\dfrac{4!}{4!}(0.538)^4=1-(0.538)^4\approx 0.916[/tex]
