Probability – Basic/Theoretical
The probability of an event is the ratio of favorable outcomes to the total number of equally likely outcomes.
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The formula is P(event) = number of favorable outcomes ÷ total number of outcomes. The sample space is the set of all possible results.
Probability is always a number between 0 and 1 (inclusive). A probability of 0 means the event is impossible; a probability of 1 means it is certain. You can express any probability as a fraction, a decimal, or a percent.
Theoretical probability is calculated by counting outcomes — what should happen based on the math. For a fair coin, theoretical P(heads) = 1/2, because there is one favorable outcome out of two equally likely outcomes.
Worked example
A bag has 3 red and 7 blue balls. What is P(red)?
- Count the favorable outcomes — red balls: 3.
- Count the total outcomes — all balls: 3 + 7 = 10.
- Apply the formula: P(red) = 3/10 = 0.3 = 30%.
- Check: P(red) + P(blue) = 3/10 + 7/10 = 1. All probabilities in the sample space sum to 1.
P(red) = 3/10 = 0.3 = 30%
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