What Are the Chances? Theoretical Probability

Imagine you reach into a bag without looking. Inside there are 3 red counters and 7 blue counters — 10 counters in total. Someone offers you a prize if you pull out a red counter first try. Would you take the bet? Before you decide, you need a way to measure how likely something is. That measurement is called probability, and by the end of this lesson you will be able to calculate it exactly — no guessing required.

Theoretical probability is the probability we calculate using logic and counting — before we run any experiment. It tells us what should happen in a perfectly fair situation. The formula is: P(event) = number of favourable outcomes ÷ total number of possible outcomes P(event) is notation meaning 'the probability of the event happening'. A favourable outcome is any outcome that counts as a success for the event you are interested in. Total possible outcomes is every equally likely result that could happen. The result is always a number between 0 and 1 (inclusive). P = 0 means impossible; P = 1 means certain. You can express probability as a fraction, a decimal, or a percentage — they all say the same thing in different forms. Probability also lets you make predictions. If you repeat an action many times, the expected number of successes is: Expected frequency = P(event) × number of trials This is called the expected frequency.