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
1 · Read
The trials in this lesson have a finite list of possible outcomes, like the colours on a spinner. Finite means the list ends. Exactly one outcome happens in each trial. If the list includes every possible outcome, their probabilities add to 1. Together they make a whole. To find one missing chance, add the known chances and subtract their total from 1.
P(A) means the probability of event A. Sometimes you want the chance that A does not happen, like not landing on red. Use P(not A) = 1 − P(A). Take the chance of A away from 1, and you get the chance of everything else.
A spinner has 8 equal sections and 1 of them is gold, so P(gold) = 1/8. To find P(not gold), subtract from 1: 1 − 1/8 = 7/8. Seven of the eight sections are not gold.
You never need to count every 'not' outcome by hand. Subtract the event's probability from 1.
All outcomes together always add to 1, so P(not A) = 1 − P(A).
The reading 'Statistics and probability FAQ' adapts Khan Academy. 'All the chances make one whole', 'Finding the one that is missing', 'The complement rule' and twelve practice questions were written for os-taxonomy. The Khan Academy video 'Simple probability: non-blue marble' is linked. Source-version license terms are unknown.
2 · Watch
Take it off screen
Where it sits
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.