Each of four persons, named 1, 2, 3, 4 fires one shot at a target. Let Ak denote the event that person k hits the target, where k = 1, 2, 3, 4. Assume A1, A2, A3, A4 are independent events. If P(A1) = 0.7, P(A2) = 0.7, P(A3) = 0.9, P(A4) = 0.4, find the probability that
a) all of the persons hit the target,
b) exactly one person hits the target,
c) no one hits the target,
d) at least one person hits the target,
e) Are events A2 and A4 mutually exclusive?