Theoretical probability comes from counting equally likely outcomes. Experimental probability comes from what actually happened: the number of times the event happened over the number of trials. To predict, multiply the theoretical probability by the number of trials: a fair dice rolled 60 times should give about 60 ÷ 6 = 10 sixes. Real results wobble around the expected number, and the wobble matters less when there are more trials.
Explore this idea with maths tools
Maths you can move
Build 8 + 5
Tap two gold counters to fill the ten-frame.
8 in the frame + 5 waiting. The total stays the same.
Words to know
- trial
- one go of an experiment, such as one toss
- experimental probability
- times it happened ÷ number of trials
- expected number
- probability × number of trials
Worked examples
A coin was tossed 20 times and landed heads 13 times. Experimental P(heads)?
- 1.Use the results: 13 heads out of 20 tosses.
- 2.13/20.
= 13/20
A spinner has 5 equal sections, 2 red. It is spun 50 times. How many reds do you expect?
- 1.P(red) = 2/5.
- 2.50 ÷ 5 × 2 = 20.
= 20
A spinner with 4 equal sections (1 red) is spun 40 times and lands on red 14 times. How many more than expected?
- 1.Expected: 40 ÷ 4 = 10.
- 2.14 − 10 = 4.
= 4
For parents
Method: Results out of trials; probability × trials
What to say: Is this from the results, or from theory? What would you expect, and what happened?
Common mistakes:
- Gives the theoretical probability instead of the result of the experiment.
- Gives the number of times the event happened instead of a probability.
- Compares successes with failures instead of with all trials.
- Uses the number of times the event did not happen.
- Expects the event half the time because it 'either happens or not'.
- Uses one favourable outcome when several give the event.
- Gives the expected number of times the event does not happen.
- Gives the expected number instead of comparing it with the result.
- Expects the event half the time when working out the difference.
- Uses one favourable outcome when working out the expected number.