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:

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

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