Relative frequency and uncertainty
Objective. Use repeated evidence to assess model reliability.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
Relative frequency and uncertainty uses repeated trials to estimate an unknown probability, calculated as the number of successes divided by the number of trials, and recognises that estimates improve with more trials. A small number of trials can give a relative frequency far from the true probability, so judgements about fairness or reliability should reference the sample size used. Comparing relative frequencies from different trial sizes shows how estimates settle closer to a theoretical value as trials increase. If a coin lands heads 58 times out of 100, the relative frequency is 0.58, suggesting possible bias worth further testing. Larger trial counts give more trustworthy evidence about long-run behaviour.
Worked example
A dice is rolled 200 times and lands on six 48 times. Find the relative frequency of rolling a six.
- 1Relative frequency = successes ÷ trials
- 2Relative frequency = 48/200
- 3Simplify the fraction
- 4Relative frequency = 0.24
Answer: 0.24
Concept mastery
Based on your past attempts at this lesson — the question types to practise again come first.
Complete a practice set to see your concept breakdown here.
Practice
Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.
Start practisingCommon mistake. A frequent error is treating a relative frequency from very few trials, such as 3 out of 5, as a precise and reliable probability, when such small samples give highly unstable estimates.
Your progress
Tick each step as you finish it. Your exact reading position is saved automatically, so Continue drops you back on the same line.
0 of 5 steps complete
Your place saves automatically as you read.