Experimental probability and relative frequency
Maths · Key Stage 3 · The School
Relative frequency
RELATIVE FREQUENCY = number of times something happened ÷ total number of trials. Toss a coin 50 times and get 28 heads: relative frequency of heads = 28/50 = 0.56. This is an ESTIMATE of the true probability, based on what actually happened, not a calculation from equally likely outcomes.
Why more trials matter
With only 10 tosses, getting 7 heads (0.7) is not unusual by chance alone, even for a fair coin. With 1,000 tosses, a result far from 0.5 would be a much stronger sign something is actually biased. More trials smooth out the effect of a short unlucky or lucky run, so the relative frequency tends to settle closer to the true probability.
Experimental vs theoretical
THEORETICAL probability is calculated from equally likely outcomes, like a fair die giving 1/6 for each number. EXPERIMENTAL probability comes from actually carrying out trials and counting results. They should be close for a fair object over many trials — and when they consistently are not, that is genuine evidence the object is not fair.
A die is rolled 300 times. A six comes up 80 times. Relative frequency of six = 80/300 = 0.267. A fair die's theoretical probability of a six is 1/6 = 0.167. The experimental result is noticeably higher than the theoretical one, and 300 trials is enough that this is unlikely to be chance alone — good evidence the die is biased towards six. If the same die had been rolled only 6 times and landed on six twice, 2/6 = 0.33 would prove almost nothing, because six rolls is far too few trials to tell luck from bias.