Probability and expected outcomes

Maths · Probability. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

Test this topic freeAll Maths topics

The idea

Probability measures how likely an event is, on a scale from 0 (impossible) to 1 (certain). It can be written as a fraction, a decimal or a percentage. When all outcomes are equally likely, the probability is the number of outcomes you want divided by the total number of outcomes.

When outcomes are not equally likely, for example with a biased spinner, we estimate the probability from an experiment. This estimate is the relative frequency. It gets closer to the true probability as the number of trials increases, so more trials give a more reliable estimate.

Outcomes that cannot happen together are mutually exclusive. If a list of such outcomes covers every possibility, their probabilities add up to 1.

Rules to remember

Common mistake

Thinking a small experiment proves bias, or that a result is 'due' after a run of the other result. Each trial of a fair coin or dice is independent, and only a large number of trials gives a reliable estimate.

Worked example

A spinner can land on red, blue or yellow only. P(red) = 0.25 and P(blue) = 0.45. The spinner is spun 200 times. How many times would you expect it to land on yellow?

  1. P(yellow) = 1 − (0.25 + 0.45) = 1 − 0.7 = 0.3.
  2. Expected number = probability × number of spins = 0.3 × 200.
  3. 0.3 × 200 = 60.

Answer: 60 times

Ask about this

Type what you are stuck on. The helper finds the explanation, worked examples and the notes to read, free and instant.

Keep going

← VectorsCombined events and conditional probability →Take a Maths test