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

step-by-step explanation:

the correct answer is the second option