Short Answer 
Mutually exclusive events cannot occur simultaneously, meaning if one event happens, the other cannot. To determine if two events A and B are mutually exclusive, check if the probability P(A AND B) is zero; if not, they can occur together, confirming they are not mutually exclusive.
Step 1: Understand Mutually Exclusive Events
Mutually exclusive events are defined as events that cannot occur at the same time. If one event happens, the other cannot. For events A and B to be mutually exclusive, the probability of both events occurring together, represented as P(A AND B), must be equal to zero.
Step 2: Analyze the Probabilities
To determine if events A and B are mutually exclusive, compare the value of P(A AND B) with zero. If P(A AND B) ‚a† 0, it indicates that both events can occur simultaneously, proving they are not mutually exclusive. In the context of your problem, check the values of:
- P(A)
- P(B)
- P(A AND B)
Step 3: Interpret the Results
After analyzing the probabilities, if you find that the product of P(A) and P(B) is not equal to P(A or B), it confirms that events A and B are not mutually exclusive. In this case, since P(A AND B) is greater than zero, it indicates that both events can happen together, resulting in the correct conclusion that events A and B are not mutually exclusive.