Final answer:
The events A and B cannot be mutually exclusive because P(A OR B) is greater than the sum of their individual probabilities. Since P(A) + P(B) = 7/10 while P(A OR B) = 9/10, the events are neither mutually exclusive nor independent.
Step-by-step explanation:
To determine whether events A and B are mutually exclusive, we need to check if the probability of both events happening at the same time is zero. In mathematical terms, if A and B are mutually exclusive, then P(A AND B) = 0. Consequently, the probability of either A or B occurring, denoted by P(A OR B), would be the sum of their individual probabilities: P(A) + P(B).
Given that P(A) = 2/5 and P(B) = 3/10, the sum of these probabilities is P(A) + P(B) = 2/5 + 3/10 = 4/10 + 3/10 = 7/10.
The provided probability of A or B occurring is P(A OR B) = 9/10, which is higher than 7/10. Therefore, the events A and B cannot be mutually exclusive because their combined probability exceeds the sum of their individual probabilities. Hence, we can conclude that the events are neither mutually exclusive nor independent.