(Solved): Please use conditonal probability/bayes theorem to solve (solution should be an actual value). Thank ...

For families in the U.S. with at least one child, assume that any such family has exactly \( k \) children with probability \( (1 / 2)^{k}, k=1,2, \ldots . \) Also, assume the probability that any child is male is equal to \( 1 / 2 \). (a) For U.S. families with at least one child, find the probability of the event "no male children." (b) For U.S. families with at least one child, find the probability of the event "at least one male child and at least one female child." (c) It is known that a randomly chosen U.S. family has at least one male and one female child. Find the probability that his family has at most three children.