I. Theorem of Complementary Events
Two events are said to be complementary events if the sum of their probability is 1. Thus, if A is an event and the probability of A is given by P(A) then this theorem states that
P(A’) = 1 – P(A)
where P(A’) is the probability of the complementary event of A; i.e., A’. In such cases, events A and A’ are said to be mutually exhaustive also.
Example:
Consider an event A that 3 will appear on rolling a dice. Calculate the probability of not getting a 3.
Solution:
Probability of getting a 3 on dice =
The probability of A’ which is the probability of not getting a 3 is calculated using the theorem of complementary events as follows:
P(A’) = 1 – P(A)