Theoretical probability

Toss a coin. You know what can happen (heads or tails), but not what will happen. That is a random experiment, and each possible result is an outcome.

Equally likely means no outcome has any reason to come up more often than another: heads or tails on a fair coin, the six faces of a fair die.

Not everything is equally likely. A bag has 4 red balls and 1 blue. The outcomes 'red' and 'blue' are not equally likely, because red has 4 chances to blue's 1. Treat each ball as one outcome instead: 5 equally likely balls, 4 of them red.

Why we need theory. In Class 9 you found probability by doing an experiment many times. But you can't launch a satellite or wait for an earthquake a thousand times just to count. So we work it out instead.

Theoretical probability (given by Laplace in 1795):

P(E) = (number of outcomes favourable to E) ÷ (number of all possible outcomes)

It works only when the outcomes are equally likely.

Example: a die is thrown once. P(a number greater than 4): the favourable outcomes are 5 and 6, so 2 out of 6, giving 1/3.

An elementary event has just one outcome (getting a 3). The probabilities of all the elementary events add up to 1: on a die, 1/6 six times.