A swimming pool has two pumps to circulate water. Denote the event that the first pump fails by A and the event that the second pump fails by B. Experimental testing has shown that the probability of A is 0.02, and the probability of B given that A has occurred is 0.15; while the probability of B given that A has not occurred is 0.05. (a) Express the given information in probability notation. (b) Calculate P(B). (c) Hence, or otherwise, are the events A and B independent? Explain your answer without performing any further calculations. (d) Find P(A/B). (e) Without calculating it, what does P(ANB) mean in context?