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