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marishachu [46]
3 years ago
5

In a certain​ country, the true probability of a baby being a girl is 0.469. Among the next seven randomly selected births in th

e​ country, what is the probability that at least one of them is a boy​?
Mathematics
1 answer:
-BARSIC- [3]3 years ago
8 0

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}

Where, ^nC_x=\frac{n!}{x!(n-x)!}

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}

=0.00499125661758

Hence, the probability that at least one of them is a boy​ = 1 - P(X=7)

= 1 - 0.00499125661758

= 0.995008743382

≈ 0.995

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