Probability for beginners: how to find the chance of something happening

Probability is a number that says how likely something is. It is written as a fraction, a decimal or a percentage, and it always sits between 0 and 1.

The scale

• 0 means it cannot happen (rolling a 7 on a normal die).
• 1 means it is certain (the sun rising tomorrow, in a school problem).
• Anything in between: the closer to 1, the more likely.

The formula

When every outcome is equally likely:

Probability = number of ways it can happen ÷ total number of outcomes

Worked examples

1. A die. What is the probability of rolling a number greater than 4 on a fair die? The numbers 5 and 6 work, that is 2 out of 6, so the probability is 2/6 = 1/3.

2. A bag of balls. A bag has 3 red and 5 blue balls. There are 8 balls in all, so the probability of picking red is 3/8.

3. The word NOT. In the same bag, the probability of not picking red is 5/8. The chances of "red" and "not red" always add up to 1: 3/8 + 5/8 = 1.

4. A coin. The probability of heads is 1/2.

5. Playing cards. A pack has 52 cards, 26 red and 26 black. The probability that a card picked at random is red is 26/52 = 1/2.

6. Two coins. Toss a coin twice. The equally likely results are HH, HT, TH and TT. The probability of at least one head is 3 out of 4, so 3/4.

Write it as a fraction, then simplify

Count the ways, count the outcomes, write the fraction, then simplify. 2/6 becomes 1/3 because both numbers divide by 2. Keep the answer as a fraction unless the question asks for a decimal or a percentage.

Mistakes to avoid

• Counting the wrong total. In the bag example the total is 3 + 5 = 8, not 5 or 3.
• Forgetting "equally likely". The formula only works when each outcome has the same chance. A spinner with unequal sections needs a different approach.
• Writing a probability bigger than 1. If your answer is 5/3, check your counting.
• Thinking the past changes the next toss. A fair coin that landed heads three times still has a probability of 1/2 for heads on the next toss.

Practise it

• Probability practice online with instant feedback and a mastery score.
• Probability worksheets with an answer key.
• An interactive probability lesson where you run experiments.

Common questions

What is the difference between probability and chance?

They mean the same in everyday talk. In maths, probability is the number from 0 to 1 that measures the chance.

Can probability be a percentage?

Yes. 1/2 is 50% and 1/4 is 25%. Use whichever form the question asks for.

What does it mean if the probability is 0.5?

The event is as likely to happen as not to happen, like heads on a fair coin.

Which grade learns probability?

Usually Grade 6 to Grade 8 (Class 6 to 8), with simple ideas introduced earlier.

This guide is general information. For exams, follow your school, teacher and official exam board, and use your own judgement about what suits your child.