The Complement Rule
The complement of an event is the probability that the event does not occur, or the probability of all other events occurring combined [6]. This is usually denoted as P(A’) or P(Ac) (read as “not A”) [7].
"Oh! So if the probability of it raining today is 90% (or 0.9), then the probability that it will not rain or the complement P(A’) is 10% (0.1)"
This makes sense because the sum of all the probabilities for all possible events is equal to 1, the probability of an event occurring P(A) and the probability of an event not occurring P(A’) sums up to 1, i.e. P(A) + P(A’) = 1 [6].
The complement rule is used to calculate the probability of the complement, by rearranging the above equation to get P(A’) = 1 - P(A) [6, 7].
Let’s take a look at an example together! Hover to reveal the answer. ​​
You entered a draw for a mystery fruit in a box containing 10 different fruits, one of them being an apple. Because you went apple picking the past week and ate way too many apples, you hope to draw any fruit but an apple from the box. What is the probability that you do not draw an apple?
​
Hover to reveal the answer...
Using the complement rule, P(not apple) = 1 - P(apple)
Since you know that there is 1 apple and 10 fruits in total, P(apple) = 1/10
Therefore, P(not apple) = 1 - 1/10 = 9/10
You will have a 9 in 10, or 90% chance of not drawing an apple from the mystery box!
In this learning module we have covered some of the foundational probability concepts and rules. Now you will be able to understand how certain probabilities used in research are derived and calculated. Remember the three main rules we have learned:
1) Addition Rule → probability of at least one event occurring
2) Multiplication Rule → probability of one event and another event occurring
3) Complement Rule → probability of an event not occurring
About Us
Science for Everyone is a Canadian Nonprofit Organization that provides educational resources to help raise the level of scientific literacy in the general population.