Sample space and events
The sample space is the list of every possible outcome. An event is a group of outcomes you care about. Probability is the number of outcomes in the event divided by the total, when all outcomes are equally likely.
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Analogy
The sample space is the whole menu. An event is the set of dishes you would be happy to order.
Example
Outcomes: 6 x 6 = 36Event: sum is 7(1,6) (2,5) (3,4) (4,3) (5,2) (6,1)6 outcomesP(sum 7) = 6 / 36 = 1/6
In practice
Insurers, games and weather forecasts all start by listing what can happen.
Questions people ask
What is the range of a probability?
A probability is always between 0 and 1. Zero means the event cannot happen and 1 means it is certain. People often write probabilities as percentages, so 0.25 is 25 percent. A value below 0 or above 1 signals a calculation mistake.
What does equally likely outcomes mean?
It means each outcome has the same chance, like the six faces of a fair die. The counting formula (favourable divided by total) only works then. A loaded die or a biased coin breaks the assumption, and you need measured probabilities instead.