Problem 2.64 Let Wi, i = 1, 2, 3 denote the event that component i is working. W i de[1]notes the event that the ith component is not working. Assume the events Wi, i = 1, 2, 3 are mutually independent and P(Wi)=0.9, i = 1, 2, 3. Compute the probabilities of the following events: Of the components W1, W2, W3

(a) only W1 is working

(b) all three components are working

(c) none are working

(d) at least one is working

(e) at least two are working (f ) exactly two are working