(a) The inclusion-exclusion principle for three events A, B, and C is P(A[B[C) = P(A)+P(B)+P(C)-P(A\B)-P(A\C)-P(B\C)+P(A\B\C)
Prove this result.
(b) Suppose three fair dice are rolled. Use part (a) to calculate the probability that at least one even number is observed.