Find the probability that in a family of 3 children chosen at random there are 2 boys given that the first child is a boy.
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Answer:
list all possibilities for the sequential birth of 3 children: GGG, GGB, GBG, GBB, BGG, BGB, BBG, BBB
count up those that have exactly 2 boys: GBB, BGB, BBG
the desired probability is 3/8.
Explanation:
Presumably the author is not including the possibility of having identical twins or multiples, which skews the straightforward probability, but is also small enough to be negligible. Furthermore, the author is presumably assuming an equal probability of boy or girl at birth (not actually biologically true as some commenters point out below).
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