How do you calculate probability?
Short answer
Probability = number of favourable outcomes ÷ total number of equally likely outcomes. It is always between 0 (impossible) and 1 (certain), and can be written as a fraction, decimal or percentage. The probability of an event not happening is 1 minus the probability that it happens.
Step by step
- Count all the possible outcomes, making sure they are equally likely.
- Count the outcomes you want.
- Divide the outcomes you want by the total and simplify.
- For two independent events both happening, multiply their probabilities.
- For either of two outcomes that cannot happen together, add their probabilities.
Worked example
A bag has 3 red, 5 blue and 2 green counters. One is taken at random.
- Total: 3 + 5 + 2 = 10
- P(blue) = 5/10 = 1/2
- P(not green) = 1 − 2/10 = 8/10 = 4/5
Common mistakes
- Giving a probability greater than 1.
- Forgetting to reduce the total when an item is not replaced.
- Adding probabilities when both events must happen. Use multiplication for and.
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