1. Let ? = {a, b, c, d, e, f }. Assume that m(a) = m(b) = 1/8 and m(c) = m(d) = m(e) = m(f ) = 3/16. Let A, B, and C be the events A = {d, e, a}, B = {c, e, a}, C = {c, d, a}.
Show that P (A ∩ B ∩ C) = P (A)P (B)P (C) but no two of these events are independent.
2. What is the probability that a family of two children has
(a) two boys given that it has at least one boy?
(b) two boys given that the first child is a boy?