Question

Out of 800 families with 5 children each how many would you expect to have i) 3boys ii) 5 girls iii) at least one boy. Assume equal probabilities for boys and girls

Answer 1

Explanation:

The probability of having a boy or a girl is 0.5. Using the binomial distribution formula, we can calculate the probabilities for (a) and (b):(a) The probability of having exactly 3 boys in a family is:P(3 boys) = (5 choose 3) * (0.5)^3 * (0.5)^2 = 0.3125 where (5 choose 3) is the number of ways to choose 3 boys out of 5 children.There are 800 families, so the expected number of families with 3 boys is:800 * 0.3125 = 250 Therefore, we would expect 250 families to have exactly 3 boys.(b) The probability of having either 2 or 3 boys in a family is:P(2 or 3 boys) = P(2 boys) + P(3 boys)where P(2 boys) is the probability of having exactly 2 boys in a family:P(2 boys) = (5 choose 2) * (0.5)^2 * (0.5)^3 = 0.3125 and P(3 boys) is the same as before.So, P(2 or 3 boys) = 0.3125 + 0.3125 = 0.625The expected number of families with either 2 or 3 boys is:800 * 0.625 = 500 Therefore, we would expect 500 families to have either 2 or 3 boys.

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