Probability Distributions

Probability Distributions

GCSE(F), GCSE(H),

Relative frequency relates directly to trials taking place (as part of an experiment, or measuring practical results).

Relative frequency = `frac(text(number of indicative trials))(text(total number of trials))` where the indicative trial is the trial that is being measured; for example, measuring the number of 6s when throwing a dice.

To improve the accuracy of the relative frequency obtained by a set of trials, increase the number of trials being conducted. For example, 1000 trials will give a far more accurate value of a relative frequency than 20 trials.

Examples

1. Sam has written a computer program that generates a random number. The random numbers are always 1, 2, 3, 4 or 5. The results are shown below after he had tested it 200 times.

12345
frequency3836322569

Is the random number generator truly random?

Answer: No

There appears to be a bias towards 5 being generated.

2. A d12 (12-sided) dice is known to be biased. It is rolled 1000 times. A 12 is obtained 78 times. What is the relative frequency for throwing a 12?

Answer: 0.078

Relative frequency = `frac(text(number of indicative trials))(text(total number of trials))`

relative frequency = `frac(78)(1000)` = 0.078