Appears in: Functional Skills Level 1 · Functional Skills Level 2 · GCSE foundation
Probability: how to work it out
Probability is a number between 0 (impossible) and 1 (certain) that says how likely something is. Level 1 asks you to place events on that scale and work out simple probabilities. Level 2 and GCSE foundation add 'not', expected numbers and combined events. Nearly every question starts with the same fraction.
The method
- Probability of an event = number of ways it can happen ÷ total number of equally likely outcomes. Write it as a fraction, then simplify or convert if asked.
- Probability of something not happening = 1 − probability that it does. All the probabilities of what can happen add to 1.
- Expected number = probability × number of trials.
- For two independent events both happening, multiply their probabilities. For two events that can't both happen, add.
- List outcomes systematically (a sample space) when there are two things happening — two coins, a coin and a dice — so nothing is missed.
Worked examples
Example 1
A bag has 3 red and 5 blue counters. One is picked at random. What is the probability it is red?
- Ways to get red: 3. Total counters: 8.
- P(red) = 3/8.
Example 2
Using the same bag, what is the probability the counter is not red?
- P(not red) = 1 − 3/8 = 5/8. (Or count: 5 blue out of 8.)
Example 3
A spinner has a probability of 0.15 of landing on 'win'. If it is spun 400 times, how many wins would you expect?
- Expected wins = 0.15 × 400 = 60.
Example 4
A fair coin is flipped and a fair dice is rolled. What is the probability of a head and a six?
- P(head) = 1/2 and P(six) = 1/6. The events are independent, so multiply.
- 1/2 × 1/6 = 1/12.
Example 5
Two fair coins are flipped. What is the probability of getting exactly one head?
- List the outcomes: HH, HT, TH, TT — four, equally likely.
- Exactly one head: HT and TH, so 2 out of 4 = 1/2.
Where the marks go missing
- Writing a probability as '3 in 8' or '3 : 8' when a fraction, decimal or percentage is asked for. 3/8, 0.375 or 37.5%.
- Giving a probability bigger than 1, or negative. If that happens, the fraction is upside down.
- Adding when the question means 'both' (multiply), or multiplying when it means 'either' (add).
Frequently asked questions
How do you work out probability?
Divide the number of ways the event can happen by the total number of equally likely outcomes. Rolling a 3 on a fair dice: one way out of six, so 1/6.
How do you work out the probability of something not happening?
Subtract the probability that it does happen from 1. If P(rain) = 0.3, then P(no rain) = 0.7.