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1. Some couples planning a new family would prefer at least one child of each sex....

1. Some couples planning a new family would prefer at least one child of each sex. The probability that a couple’s first child is a boy is 0.512. In the absence of technological intervention, the probability that their second child is a boy is independent of the sex of their first child, and so remains 0.512. Imagine that you are helping a new couple with their planning. If the couple plans to have only two children:
(a) What is the probability of getting one child of each sex? [5]
(b) What is the probability that at least one girl is born? [5]
(c) What is the probability that at least one boy is born? [5] and (d) What is the probability that both children are the same sex? [5]

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