Two events are described as complementary if they are the only two possible outcomes.
For example, imagine we are testing whether it rains on a particular day.
The events "it rains" and "it doesn't rain" are complementary because:
 only one of the two events can occur
 no other event can occur
Therefore, these two events are complementary.
For another example, consider the rolling of a die to see whether the result is odd or even.
The events "odd" and "even" are complementary because:
 the result must be either "odd" or "even" (not both)
 the result cannot be anything except "odd" or "even"
Therefore, these two events are also complementary.
Finally, consider a bag only containing 4 white balls and 5 black balls.
We are interested in whether a ball picked from the bag is white or black.
The events "white" and "black" are complementary.
The probability of "white" is p(white) = .
The probability of "black" is p(black) = .
Notice how p(white) + p(black) = 1.
p(A) + p(A') = 1 
So, to find the probability an event not happening, we need to subtract the probability of that event from 1.
Practice Questions
Work out the answers to these questions then click
to see whether you are correct.
(a) The probability of Jane winning her tennis match is  .  
(b) A spinner only has whole numbers as outcomes. The probability of getting an even number is 0.27.
What is the probability of getting an odd number?
Some of the answers in this section are fractions. Each fraction has two input boxes. Put the numerator in the top box and the denominator in the bottom box, like this: 
