Which part(s) of events is (are) independent?
A and B given the following: P(A) = 0.3, P( A and B)= 16 C and D given the following: P(C) = 0.4, P(D) = 0.3, P(C given D has occurred)=0.4
In the case of A and B, we are only given the probability of A and B occurring together, P(A and B). We do not have separate probabilities for P(A) and P(B), so it is not possible to determine if A and B are independent.
In the case of C and D, we are given the probability of C occurring, P(C), the probability of D occurring, P(D), and the conditional probability of C given D has occurred, P(C given D has occurred). Since we have these separate probabilities, we can determine if C and D are independent.
Two events C and D are independent if and only if P(C and D) = P(C) * P(D).
From the given information, we know that P(C) = 0.4 and P(D) = 0.3. However, we do not have the probability of C and D occurring together, P(C and D). Therefore, we cannot determine whether C and D are independent.