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7.2 Probability of the Complement of an Event

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7.2 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 ) = 6 40 = 3 20 ∴ P ( A ' ) = 1 − P ( A ) = 1 − 3 20 = 17 20 Hence, the probability that the number chosen is not a perfect square is 17 20 .