Determine if the event A and B are mutually exclusive, independent, or neither.

Question

P(A)=0.38, P(B)=0.42, P(A or B) = 0.78

Answer 1

To determine whether the events A and B are mutually exclusive, independent, or neither, we can use the following definitions:

- Mutually exclusive events: Mutually exclusive events are events that cannot occur at the same time. If events A and B are mutually exclusive, then P(A or B) = P(A) + P(B).

- Independent events: Independent events are events where the occurrence of one event does not affect the occurrence of the other event. If events A and B are independent, then P(A and B) = P(A) * P(B).

Given that P(A) = 0.38, P(B) = 0.42, and P(A or B) = 0.78, we can plug these values into the formulas:

P(A or B) = P(A) + P(B)
0.78 = 0.38 + 0.42

Since 0.78 is equal to the sum of P(A) and P(B), the events A and B are mutually exclusive.

So the answer is mutually exclusive.