Because the total probability for a sample space must be equal to 1, the probabilities of complementary events must sum to 1.

In symbols, p(A)+p(A^{C})=1.

As a result, p(A^{C})=1-p(A).

In words, the probability that an event does not happen is equal to one minus the probability that it does.

If
the probability of an event is , what is the probability of its complement?

The probability of its complement is

A number is chosen at random from a set of whole numbers from 1 to 50. Calculate the probability that the chosen number is not a perfect square.

Let *A* be the event of choosing a perfect square.

Let *A*^{C} be the event that the number chosen is not a perfect square.

*A* = {1, 4, 9, 16, 25, 36, 49}

Number of elements in *A*, *n*(*A*) = 7

Total number of elements, *n*(*S*) = 50

The probability that the number chosen is not a perfect square is