Question

Select the correct answer.

Two events, E1 and E2, are defined for a random experiment. What is the probability that at least one of the two events occurs in any trial of the experiment?

A.
P(E1) + P(E2) − 2P(E1 ∩ E2)

B.
P(E1) + P(E2) + P(E1 ∩ E2)

C.
P(E1) − P(E2) − P(E1 ∩ E2)

D.
P(E1) + P(E2) − P(E1 ∩ E2)

Answer 1

The correct answer is:

D. P(E1) + P(E2) − P(E1 ∩ E2)

The probability that at least one of the two events occurs in any trial of the experiment is equal to the sum of the probabilities of each event (P(E1) and P(E2)), minus the probability of both events occurring simultaneously (P(E1 ∩ E2)). This ensures that we do not double-count the probability of both events happening at the same time.

Step-by-step explanation:

Answer 2

Answer: Choice D

Step-by-step explanation:

The portion P(E1)+P(E2) computes the probability of either event occurring. We subtract off P(E1 ∩ E2) to avoid double-counting the overlapped region.

If E1 and E2 are disjoint or mutually exclusive, then P(E1 ∩ E2) = 0.