9.2 Probability of the Complement of an Event
1. The complement of an event A is the set of all the outcomes in the sample space that are not included in the outcomes of event A.
2. The probability of the complement of event A is:
P(A')=1−P(A)
Example:
A number is chosen at random from a set of whole number from 1 to 40. Calculate the probability that the chosen number is not a perfect square.
Solution:
Let
A = Event of choosing a perfect square.
A’ = Event that the number is not a perfect square.
A = {1, 4, 9, 16, 25, 36}
n(A) = 6
P(A)=n(A)n(S)=640=320∴P(A')=1−P(A)=1−320=1720Hence, the probability that the number chosenis not a perfect square is1720.