Answer:
The probability that at least one of 8 babies born is a girl is 0.9954.
Step-by-step explanation:
Let X = a baby born is a girl.
The probability of a baby born being a girl is,
P (G) = 1 - P (B)
= 1 - 0.511
p = 0.489
The number of births is, n = 8.
The random variable X follows a Binomial distribution with parameters n and p.
The probability mass function of the Binomial distribution is:
[tex]P(X=x)={8\choose x}0.489^{x}(1-0.489)^{8-x};\ x=0,1,2,3...[/tex]
Compute the probability that out of 8 births at least one is a girl as follows:
P (X ≥ 1) = 1 - P (X < 1)
= 1 - P (X = 0)
[tex]=1-{8\choose 0}0.489^{0}(1-0.489)^{8-0}\\=1-(1\times1\times 0.00465)\\=1-0.00465\\=0.99535\\\approx 0.9954[/tex]
Thus, the probability that at least one of 8 babies born is a girl is 0.9954.
