Question

In a certain​ country, the true probability of a baby being a boy is 0.522. Among the next five randomly selected births in the​ country, what is the probability that at least one of them is a girl​?

Answer 1

Answer: 0.9612

Explanation:

The binomial distribution formula is given by :-

`P(x)=^nC_xp^x(1-p)^(n-x)`, 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 :
`p=1-0.522=0.478`

Number of trials : n= 5

Now, the required probability will be :

`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`

Thus, the probability that at least one of them is a girl​ = 0.9612