Calculating Simple Probabilities

In a Nutshell

For equally likely outcomes, P(event)=number of favourable outcomestotal number of outcomesP(\text{event}) = \dfrac{\text{number of favourable outcomes}}{\text{total number of outcomes}}.

When every outcome is equally likely — like rolling a fair die or spinning a fair spinner — we can calculate the probability of an event with a simple fraction.

For example, a fair six-sided die has outcomes {1,2,3,4,5,6}\{1, 2, 3, 4, 5, 6\}. The probability of rolling a 4 is:

P(4)=16P(4) = \frac{1}{6}

If an event can happen in more than one way, count all the favourable outcomes. The probability of rolling an even number is:

P(even)=36=12P(\text{even}) = \frac{3}{6} = \frac{1}{2}

because three of the six faces (2, 4, 6) are even.

Spinner wheel for probability A circular spinner divided into equal sectors, each labelled with a number. Press Spin to choose a random outcome and see the probability.

Watch it work

Question: A bag contains 3 red, 5 blue and 2 green marbles. A marble is picked at random. Find P(blue)P(\text{blue}).

Have a go

Q1. A fair spinner has 8 equal sections numbered 1–8. Find P(5)P(5).

Q2. A bag has 4 red and 6 yellow counters. One is picked at random. Find P(red)P(\text{red}).

Q3. The letters of the word MATHEMATICS are placed in a bag. One letter is chosen at random. Find the probability of choosing the letter A.

Q4. A fair die is rolled once. Find the probability of rolling a number greater than 4.