Answer:
Two events, A and B, are considered mutually exclusive if they cannot both occur at the same time. In other words, if one of them happens, the other cannot. Mathematically, for mutually exclusive events:
P(A and B) = 0
In your question, you have provided the probabilities of A and B individually (P(A) = 0.2 and P(B) = 0.4) and the probability of their union (P(A or B) = 0.5).
To determine if A and B are mutually exclusive, you need to check if the probability of their intersection (P(A and B)) is equal to 0. If P(A and B) = 0, then A and B are mutually exclusive. If P(A and B) is greater than 0, then they are not mutually exclusive.
Unfortunately, you haven't provided the value of P(A and B) in your question. To determine whether A and B are mutually exclusive, you would need to calculate or provide the value of P(A and B). If P(A and B) is 0, then A and B are mutually exclusive. If it's not 0, they are not mutually exclusive.
Explanation: