In a certain country, the true probability of a baby being a boy is 0.516. Among the next six randomly selected births in the country, what is the probability that at least one of them is a girl?

The value of the probability is 0.9811

Step-by-step explanation:

Given that the Probability (boy) = 0.516, and that the birth of a boy is mutually dependent on the birth of a girl, we can say that,

The Probability (girl) = 1 - Probability(boy).

The interpretation of the question, "at least one of them is a girl" is that:

Out of 6 births, there could be one, two, three, four, five or six (all) girls.

Finding this probability for each possibility, would be time taking. The mutually exclusive event to this is that "there will be no girls born at all"

so, we can find:

Probability (no girl at all in six births) = Probability (six boys out of six births)

= 0.516 ∧ 6 = 0.0189

Therefore,

Probability (at least one of them is a girl) = 1 - Probability (no girl at all in six births) = 1 - 0.0189 = 0.9811

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