(a) What is the probability of a 13-child family having 13 boys? (Assume
that the probability of having a boy or a girl is the same. Round answer to six decimal places.)

there are only to outcomes, either a boy or girl.. so the probability the first child is a boy, is 1/2 to find out the probability that they have 13 children in a row that are boys, you multiply 1/2 by itself 13times (that's 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 which is 1/8192)

so question 1: the probability is 1/8192

now the chances for them having the next child to be a boy, you multiply 1/2 by itself 14 times (that's 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2) which is the same as 1/2 x 1/8192 (which is 1/16384)