The Smith and Jones families live in adjacent houses that share a common yard. T

Question

The Smith and Jones families live in adjacent houses that share a common yard. The Smith family has two children, a boy and a girl. The Jones family has six children, all of whom are boys. Suppose that all the children are in the yard playing. If you pick a child at random, what is the probability that you will choose a boy? All the children are inside their appropriate houses. You pick a house at random, and then pick a child from within that house. What is the probability that this child is a boy?

Explanation / Answer

a) P(a boy) = (1+6)/(6+2) = 7/8

b) total probability = P(simith house)*P(boy of smith)+(P jones house)*P(boy of jones)

= .5*.5+.5*1 = .75 = 3/4

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