Events A and B are independent, Suppose event A occurs with probability 0.95 and event E occurs with probability 0.93.

a Compute the probability that neither the event A nor to event B occurs.

b Compute the probability that either B occurring A and B both occur.

a) 0.0035

b) 0.93

Step-by-step explanation:

P (A) = 0.95

P (E) = 0.93

Now,

P (A∩E) = P (A) * P (E) = 0.95 * 0.93

or

P (A∩E) = 0.8835

P (A∪E) = P (A) + P (E) - P (A∩E)

or

P (A∪E) = 0.95 + 0.93 - 0.8835

or

P (A∪E) = 0.9965

Therefore,

a) probability that neither the event A nor to event B occurs

P (A'∩E') = 1 - P (A∪E)

or

P (A'∩E') = 1 - 0.9965 = 0.0035

b) probability that either B occurring A and B both occur

P ((A'∩B) ∪ (A∩E)) = P (B) = 0.93