if P(A)=.60, P(A/B)=.50, AND P(B)= .40, answer the following.

1) events A and B are independent =FALSE

true or false or cannot determine

2) events A and B are disjoint =TRUE

true or false or cannot determine

3) find P(A and B) =??????

MATH-STAT

To answer these questions, we will use basic probability principles.

1) To determine whether events A and B are independent, we need to check whether the probability of event A occurring is affected by the occurrence of event B, and vice versa. If events A and B are independent, then P(A/B) should be equal to P(A). However, in this case, P(A) is 0.60 while P(A/B) is 0.50. Since the probabilities are not equal, events A and B are dependent. Therefore, the answer is FALSE.

2) Disjoint events are events that cannot occur simultaneously. In other words, if one event happens, the other event cannot simultaneously happen. To check if events A and B are disjoint, we need to confirm if their intersection (A and B) is an empty set. If P(A and B) = 0, then events A and B are disjoint since their intersection is empty. In this case, since P(A and B) is not provided, we cannot determine if events A and B are disjoint. Therefore, the answer is "cannot determine".

3) To find P(A and B), we can use the formula:

P(A and B) = P(A) * P(B/A)

The given information gives us P(A) = 0.60 and P(A/B) = 0.50. However, we also need P(B/A) to calculate P(A and B). Unfortunately, P(B) = 0.40 is not sufficient to find P(B/A), so we cannot determine the value of P(A and B). Therefore, the answer is "cannot determine".