Final answer:
Two events A and B are independent if the knowledge that one occurred does not affect the chance the other occurs. A and B are mutually exclusive events if they cannot occur at the same time.
Step-by-step explanation:
Two events A and B are independent if the knowledge that one occurred does not affect the chance the other occurs. If two events are not independent, then we say that they are dependent.
A and B are mutually exclusive events if they cannot occur at the same time. This means that A and B do not share any outcomes and P(A AND B) = 0.
For example, suppose the sample space S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Let A = {1, 2, 3, 4, 5}, B = {4, 5, 6, 7, 8}, and C= {7, 9}. A AND B = {4, 5}. P(A AND B) = and is not equal to zero. Therefore, A and B are not mutually exclusive.