Question

Given any two events, E, and E2, what does the probability PE U E2) represent?

A. Neither event occurs.
B. Both of the events occur.
C.One of the events occurs, or both occur.
D. One of the events occurs but not both.

Answer 1

The probability P(E U E2) represents the chance that at least one of the two events, E or E2, occurs, which can include both events occurring if they are not mutually exclusive.

Step-by-step explanation:

The probability P(E U E2) represents the chance that either event E or event E2 occurs, or both. This is also referred to as the probability of the 'OR' event. When two events are mutually exclusive, their occurrence does not overlap, and they cannot occur at the same time. In such a case, if A and B are mutually exclusive, then P(A OR B) = P(A) + P(B). However, if the events are not mutually exclusive, this relationship may include the intersection of events A and B, and the formula adjusts to P(A OR B) = P(A) + P(B) - P(A AND B) to account for the overlap.

For example, suppose you have two events, G and H that are mutually exclusive, and the probabilities P(G) = 0.5 and P(H) = 0.3. The probability of either G or H occurring would be P(G OR H) = 0.5 + 0.3 = 0.8. This means there is an 80% chance that either event G or event H, or both, will occur.