Answer: 0.9612
Step-by-step explanation:
The binomial distribution formula is given by :-
[tex]P(x)=^nC_xp^x(1-p)^{n-x}[/tex], where P(x) is the probability of x successes out of n trials, p is the probability of success on a particular trial.
Given : The probability of a baby being a boy= 0.522.
Then the probability of a girl : [tex]p=1-0.522=0.478[/tex]
Number of trials : n= 5
Now, the required probability will be :
[tex]P(x \geq1)=1-P(0)\\\\=1-[^{5}C_0(0.478)^{0}(1-0.478)^{5-0}]\\\\=1-[(1)(0.522)^{5}]=0.961242789206\approx0.9612[/tex]
Thus, the probability that at least one of them is a girl = 0.9612
