# 7.2 Probability of the Combination of Two Events

7.2 Probability of the Combination of Two Events

1. For two events, A and B, in a sample space S, the events AB (A and B) and A υ B
(A or B) are known as combined events.

2. The probability of the union of sets A and B is given by:

3. The probability of the union of sets A and B can also be calculated using an alternative method, i.e.

4. The probability of event A and event B occurring, P(AB) can be determined by the following formula.

Example:
Given a universal set ξ = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}. A number is chosen at random from the set ξ . Find the probability that
(a) an even number is chosen.
(b) an odd number or a prime number is chosen.

Solution:
The sample space, S = ξ
n(S) = 14
(a)
Let A = Event of an even number is chosen
A = {2, 4, 6, 8, 10, 12, 14}
n(A) = 7

(b) Let,
B = Event of an odd number is chosen
C = Event of a prime number is chosen

B = {3, 5, 7, 9, 11, 13, 15} and n(B) = 7
C = {2, 3, 5, 7, 11, 13} and n(C) = 6

The event when an odd number or a prime number is chosen is B υ C.
P(B υ C) = P(B) + P(C) – P(B C)
B C = {3, 5, 7, 11, 13}, n(B C) = 5