Experimental probability
Record, describe, and analyse the frequency of outcomes from probability experiments to develop an understanding of relative frequency as an estimate of probability
What a learner can do afterwards
- Conduct a coin-toss experiment, record results in a frequency table, and calculate relative frequencies
- Compare experimental results with theoretical probability and explain discrepancies
- Explain that for independent trials with a fixed outcome probability, larger samples usually give relative frequencies nearer that probability, without guaranteeing a closer result in any particular run.
1 · Read
Relative frequency describes observed results: the number of times an outcome occurred divided by the total number of trials. Use your own data or results someone else recorded. Write the share as a fraction, or do the division to get a decimal.
Priya uses a fair coin, so the theoretical probability of heads is 0.5. Her 12 heads in 20 tosses give 12 ÷ 20 = 0.6. To compare with theory, find the gap: 0.6 minus 0.5 is 0.1. A short run can differ from theory just by chance. An exact match can also happen; neither result proves fairness.
In independent trials, knowing one result does not change the chance of another. If the chance stays the same, larger samples usually give a relative frequency nearer that chance. A particular longer run can still be farther away.
To combine runs under the same conditions, add their outcome counts and add their trial counts. Divide the combined outcome count by the combined trial count.
Relative frequency is outcome count divided by trials. With independent trials and a fixed chance, more trials usually give a closer estimate, without a guarantee.
The rewritten readings were written for this dataset.
More to read
Comparing coin results with theory
Suppose 23 of your 50 tosses of a fair coin are heads. The relative frequency of heads is 23/50 = 0.46. The theoretical probability is 1/2 = 0.5, so the difference is 0.04.
Record heads and tails in a frequency table. Divide each count by the number of tosses to get its share. A small sample can differ from theory or match exactly. For independent tosses of that same coin, 5000 usually gives a closer estimate than 50, but not every time.
What dice results can tell you
A fair die need not give the expected share of sixes in every experiment. Eight sixes in 60 rolls gives a relative frequency of 8/60 rather than the theoretical 1/6. Chance can explain this difference; it does not prove unfairness.
Record a tally for each face. With independent rolls of the same fair die, larger samples usually reduce errors in the shares. A longer run can still be farther from 1/6. Differences in raw counts need not shrink.
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