Complementary events
Understand and apply the rule that probabilities of all mutually exclusive outcomes sum to one; use this to find the probability of a complementary event (P(not A) = 1 − P(A))
What a learner can do afterwards
- Verify that probabilities of all outcomes listed for a spinner sum to 1
- Calculate the probability of NOT rolling a 6 as 1 − 1/6 = 5/6
- Identify an error in a probability distribution where the values do not sum to 1
1 · Read
You already know that all the probabilities in a situation add up to 1. That fact lets you find the chance of not rolling a 6 without listing the other five faces. If A is one event, 'not A' means everything else that could happen instead. A and 'not A' always add up to 1, the top of the probability scale. That gives the rule P(not A) = 1 − P(A): take P(A) away from 1.
A spinner has three sections. One has a probability of 0.45, and the next has 0.25. All three probabilities must add up to 1, so the third section is 1 − 0.45 − 0.25 = 0.3.
Once you know P(A), you can find P(not A) with 1 − P(A). You don't need to know anything else about the situation.
P(not A) = 1 − P(A), because A and everything else always add up to 1.
The rewritten readings were written for this dataset.
2 · Watch
Take it off screen
Where it sits
This opens up
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
20 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.