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Probability and complement

A probability is a number from 0 to 1. In a uniform model you divide the number of favourable outcomes by the number of possible ones. The complement is what does not happen, and its probability is 1 minus the original. Relative frequency is how often something happened in an experiment. With many trials it approaches the probability, but a small experiment can differ. One six on a die is one of six outcomes.

P(A)=favourablepossibleP(A) = \frac{\text{favourable}}{\text{possible}}uniform model
P(not A)=1−P(A)P(\text{not } A) = 1 - P(A)complement

Symbols

P(A)P(A)probability of A

Example

A probability of rain of 0.3 gives dry weather 1−0.3=0.71 - 0.3 = 0.7.

12 of 30 students wear glasses: 1230=0.4\dfrac{12}{30} = 0.4.

The complement and the original probability add up to 1.
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Part of Mathematics 1P: Probability.