Probability: random experiments and equally likely outcomes

Tossing a coin, rolling a die, drawing a ball from a bag without looking: in each case, you cannot predict the result with certainty. This is called a random experiment. The possible results are called outcomes: heads or tails for the coin, the numbers 1 to 6 for the die.

Even if we cannot predict the result, we can measure the chance of each outcome with a number: its probability. It is a number between 0 and 1. Probability 0: impossible (rolling a 7 with a standard die). Probability 1: certain (rolling a number between 1 and 6). In between, every shade of "maybe".

When all outcomes have exactly the same chance, we say they are equally likely. A well-balanced die, a fair coin: every outcome has the same probability. In that case, the formula is simple: probability = number of favourable outcomes divided by number of possible outcomes. To roll a 3 with a die: 1 favourable outcome out of 6 possible, so 1/6.

Watch out for the famous trap: two outcomes does not mean a one-in-two chance! In a bag with 3 red balls and 2 blue balls, there are indeed two colours, but the probability of drawing a red one is 3/5, not 1/2, because there are more red balls. Equal likelihood has to be checked, not guessed.

A probability can be written as a fraction (1/2) or as a decimal (0.5): it is the same number. In this lesson you will learn to count outcomes, spot equal likelihood and compute your first probabilities.