Probabilities Sum to One
Understand that when all possible outcomes of a trial are listed, their probabilities must add up to 1; use this to find the probability of an event NOT happening: P(not A) = 1 − P(A); apply this shortcut to avoid counting all unfavourable outcomes directly
What a learner can do afterwards
- List all outcomes of spinning a 4-colour spinner and verify their probabilities add up to 1
- Calculate P(not rolling a 3) as 1 − 1/6 = 5/6 using the complement rule
- Spot an error in a probability table where the values don't sum to 1 and explain what's wrong
The lesson
Think about every single thing that could happen in one trial, like every color a spinner could land on. If you list every outcome and add up all their chances, the total is always 1. Something has to happen, so all the chances together make a whole.
Sometimes you want the chance that something does NOT happen, like not landing on red. There's a shortcut: P(not A) = 1 − P(A). Take the chance of A away from 1, and you get the chance of everything else.
A die has 6 sides, so P(rolling a 3) = 1/6. To find P(not rolling a 3), subtract from 1: 1 − 1/6 = 5/6. Five of the six sides are not a 3.
You never have to count every single 'not' outcome by hand. Just take the probability of the event away from 1, and you're done.
All outcomes together always add to 1, so P(not A) = 1 − P(A).
Watch it
Where it sits
This opens up
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 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.