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?
Accepted Solution
A:
Answer:The probability is 0.995 ( approx ).Step-by-step 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 = 7Thus, by the binomial distribution formula,[tex]P(x)=^nC_x(p)^x q^{n-x}[/tex]Where, [tex]^nC_x=\frac{n!}{x!(n-x)!}[/tex]The probability that all babies are girl or there is no baby boy,[tex]P(X=7)=^7C_7(0.469)^7(0.531)^{7-7}[/tex][tex]=0.00499125661758[/tex]Hence, the probability that at least one of them is a boy = 1 - P(X=7)= 1 - 0.00499125661758= 0.995008743382≈ 0.995