if P(A) =1/2 and P(B)= 2/3, can the events A and B be mutually exclusive, why or why not?
In order to determine whether events A and B can be mutually exclusive, we need to understand what mutually exclusive events mean.
Mutually exclusive events are events that cannot occur at the same time. More specifically, if events A and B are mutually exclusive, then the occurrence of event A means that event B cannot occur, and vice versa. In other words, the probability of both events A and B happening simultaneously is zero.
To determine whether events A and B are mutually exclusive, we can observe their probabilities. If P(A) + P(B) = 1, then events A and B are mutually exclusive.
In this case, P(A) = 1/2 (or 0.5) and P(B) = 2/3 (or approximately 0.67).
If we add the probabilities together: P(A) + P(B) = 0.5 + 0.67 = 1.17
Since the sum of the probabilities is greater than 1, we can conclude that events A and B are not mutually exclusive. This means that there is some overlap between A and B, and it is possible for both events A and B to occur at the same time.