Question

Describe the difference between the probability of two mutually exclusive events, two complementary events, and two events that are not mutually exclusive. Give examples of each.

Answer 1

For two mutually exclusive events, we know that the probability of intersection of these two events is zero. There are no any common elements in two mutually exclusive events. For two complementary events, the sum of probability of these two complementary events is one and the probability of intersection of these two events is zero. For two events that are not mutually exclusive, the probability of union of these two events is less than one, because some probability is assigned to the intersection of these two events.

Consider two mutually exclusive events as A and B such that P(A) = 0.3 and P(B) = 0.4, then

P(AUB) = P(A) + P(B) = 0.3 + 0.4 = 0.7 and P(A∩B) = 0

Consider two complementary events as A and A’, then P(AUA’) = 1 and P(A∩A’) = 0

For example, P(A) = 0.3, P(B) = 1 - 0.3 = 0.7, then P(AUA') = 0.3 + 0.7 = 1 an dP(A∩A’) = 0

Consider two events A and B that are not mutually exclusive, then P(AUB) = P(A) + P(B) – P(A∩B)

For example, P(A) = 0.6, P(B) = 0.5, P(A∩B) = 0.3, then P(AUB) = 0.6 + 0.5 – 0.3 = 0.8