Multiplying dependent probabilities

Use properties of dependent probability like P(A | B) * P(B) = P(A and B) to solve some tricky probability problems!
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Problem

A family plans to have three children. It is equally likely that each child will be a boy or a girl. Use the sample space of possible outcomes below to answer each of the following questions.
What is P, left parenthesis, A, right parenthesis, the probability that the first child is a girl?
What is P, left parenthesis, B, right parenthesis, the probability that the last two children are boys?
What is , the probability that the first child is a girl, given that the last two are boys?
What is , the probability that the last two children are boys, given that the first is a girl?
What is P, left parenthesis, A, space, a, n, d, space, B, right parenthesis, the probability that the first child is a girl and the last two are boys?
What is ?
What is ?
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