Final answer:
To determine if events A and B are independent, we need to verify if P(A AND B) equals P(A)P(B). With P(A) = 0.2 and P(B) = 0.25, we calculate P(A)P(B) = 0.05. Without the actual probability of P(A AND B), we can't conclude, but if P(A AND B) = 0.05, then A and B would be independent.
Step-by-step explanation:
When determining whether two events A and B are independent or dependent, we can use the key property that for two independent events, P(A AND B) should equal the product of their individual probabilities, which is P(A)P(B). Given that P(B) = 0.25 and P(B|A) = 0.25, and we are told that P(A) = 0.2, we can check if these events are independent by seeing if P(A AND B) equals P(A)P(B). According to the rule of independent events, P(A AND B) should also equal P(A)P(B).
If P(B|A) = P(B), this also suggests independence. Since P(A) = 0.2 and P(B) = 0.25, their product would be P(A)P(B) = (0.2)(0.25) = 0.05. If A and B were independent, we would have P(A AND B) = 0.05. However, we need the actual probability of P(A AND B) to verify this. If it is not given, we cannot conclude definitively, but if it is 0.05, that would support A and B being independent. If P(A AND B) is not 0.05, then A and B are dependent.