# 9.2 Probability of the Complement of an Event

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:
$\overline{)\text{}P\left(A\text{'}\right)=1-P\left(A\right)\text{}}$

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
$\begin{array}{l}P\left(A\right)=\frac{n\left(A\right)}{n\left(S\right)}\\ \text{}=\frac{6}{40}=\frac{3}{20}\\ \therefore P\left(A\text{'}\right)=1-P\left(A\right)\\ \text{}=1-\frac{3}{20}=\frac{17}{20}\\ \\ \text{Hence, the probability that the number chosen}\\ \text{is not a perfect square is}\frac{17}{20}.\end{array}$