Consider two events A and B with the probability P(A) = 0.25 and P(B) = 0.6, respectively. If it is also known that P(A or B) = 0.6. Which of the following statements is true?*1 pointA and B are both independent and mutually exclusiveA and B are neither independent nor mutually exclusiveA and B are independentA and B are mutually exclusive

To determine which statement is true, we need to understand the definitions of independent and mutually exclusive events.

1. Independent events: Two events A and B are independent if the occurrence of A does not affect the occurrence of B, and vice versa. Mathematically, this is expressed as P(A ∩ B) = P(A)P(B).

2. Mutually exclusive events: Two events A and B are mutually exclusive if they cannot occur at the same time. This means that the occurrence of A rules out the occurrence of B, and vice versa. Mathematically, this is expressed as P(A ∩ B) = 0.

Given that P(A) = 0.25, P(B) = 0.6, and P(A or B) = 0.6, we can use these definitions to determine which statement is true.

First, let's check if A and B are independent. If they were independent, then P(A ∩ B) should be equal to P(A)P(B) = 0.25 * 0.6 = 0.15. However, we can calculate P(A ∩ B) using the formula P(A ∩ B) = P(A) + P(B) - P(A or B) = 0.25 + 0.6 - 0.6 = 0.25. Since 0.25 ≠ 0.15, A and B are not independent.

Next, let's check if A and B are mutually exclusive. If they were mutually exclusive, then P(A ∩ B) should be equal to 0. However, as we calculated above, P(A ∩ B) = 0.25, which is not equal to 0. Therefore, A and B are not mutually exclusive.

So, the correct answer is "A and B are neither independent nor mutually exclusive".