Question

Event A occurs with probability 0.2. Event B occurs with probability 0.9. What must be true about events A and B?

A. Events A and B are complementary.
B. Events A and B are disjoint.
C. Events A and B cannot be disjoint.
D. Events A and B cannot be independent.

Answer 1

Events A and B cannot be disjoint and are not complementary. It is unclear whether events A and B are independent or dependent based on the given information.

The correct answer is:

D. Events A and B cannot be independent.

Step-by-step explanation:

Events A and B cannot be disjoint. Disjoint events are events that cannot occur at the same time, meaning the probability of their intersection, P(A AND B), is equal to zero. However, the question states that the probability of Event A occurring is 0.2 and the probability of Event B occurring is 0.9. Since both probabilities are greater than zero, events A and B cannot be disjoint.

Disjoint events are also known as mutually exclusive events. So, we can conclude that events A and B are not mutually exclusive.

In order for events A and B to be complementary, the sum of their probabilities must be equal to 1. However, in this case, the sum of the probabilities of events A and B is 0.2 + 0.9 = 1.1, which is greater than 1. Therefore, events A and B are not complementary.

To determine if events A and B are independent, we would need additional information about the conditional probability of one event given another. But based on the provided information, we cannot conclude whether events A and B are independent or dependent.