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There is no simple answer to this question because the genders of children depend on the parents genes and age and so are not independent events. Also, the probabilities of the two genders are not equal. Further, some of the children may be identical twins or triplets.
Assuming, however, that the genders are independent, the answer is 0.3872, approx.
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What is the probability that a family of 5 children has exactly 3 boys?
6 out of 9.
What is the probability of getting three boys out of three children?
I wouldn't say it's very probable. My neighbor has three children and they're all boys. It just depends on the mother and father.
What is the probability of exactly 7 boys in 10 births when the birth of any child does not affect the probability of the gender of any other children?
This is a Binomial Probability; p=0.5, n=10 & x=7. Since you want the probability of exactly 7, in the related link calculator, after placing in the above values, P(x=7) = 0.1172 or 11.72%.
What is the probability that a coulple with three children will have three boys?
There is no simple answer to the question because the children's genders are not independent events. They depend on the parents' ages and their genes. However, if you assume that they are independent events then, given that the probability of a boy is approx 0.52, the probability that all three children are boys is approx 0.1381
What is the probability that a family with four children has all boys given that the first two are boys?
There is no simple answer to the question because the children's genders are not independent events. They depend on the parents' ages and their genes. However, if you assume that they are independent events then, given that the probability of a boy is approx 0.52, the probability of the other two being boys is 0.2672.
