Mutually exclusive events
Objective. Use probabilities that sum to one.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
Mutually exclusive events cannot happen at the same time, such as rolling a 3 or rolling a 5 on a single die, and their probabilities can simply be added together to find the probability of either occurring. Since the probabilities of all possible outcomes in a sample space always sum to exactly 1, if you know the probability of an event you can find the probability of it not happening by subtracting from 1. Example: if the probability of rain tomorrow is 0.3, the probability of no rain is 1 − 0.3 = 0.7. This rule works because 'rain' and 'no rain' are mutually exclusive and cover every possibility.
Worked example
A bag contains coloured counters. The probability of picking red is 0.4 and the probability of picking blue is 0.25. These are mutually exclusive events, so find the probability of picking either red or blue.
- 1Mutually exclusive events cannot happen together, so their probabilities can be added.
- 2Add the two given probabilities: 0.4 + 0.25.
- 3This gives 0.4 + 0.25 = 0.65.
- 4The probability of picking either red or blue is 0.65.
Answer: 0.65
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Practice
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Start practisingCommon mistake. Pupils sometimes multiply probabilities of mutually exclusive events instead of adding them; remember that mutually exclusive outcomes use addition, since only one of them can occur at a time.
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