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 = 7
Thus, by the binomial distribution formula,
![P(x)=^nC_x(p)^x q^{n-x}](https://tex.z-dn.net/?f=P%28x%29%3D%5EnC_x%28p%29%5Ex%20q%5E%7Bn-x%7D)
Where, ![^nC_x=\frac{n!}{x!(n-x)!}](https://tex.z-dn.net/?f=%5EnC_x%3D%5Cfrac%7Bn%21%7D%7Bx%21%28n-x%29%21%7D)
The probability that all babies are girl or there is no baby boy,
![P(X=7)=^7C_7(0.469)^7(0.531)^{7-7}](https://tex.z-dn.net/?f=P%28X%3D7%29%3D%5E7C_7%280.469%29%5E7%280.531%29%5E%7B7-7%7D)
![=0.00499125661758](https://tex.z-dn.net/?f=%3D0.00499125661758)
Hence, the probability that at least one of them is a boy = 1 - P(X=7)
= 1 - 0.00499125661758
= 0.995008743382
≈ 0.995