Relative frequency

When you can't work out a probability from equally likely outcomes, estimate it from an experiment.

Relative frequency = frequency ÷ number of trials (learn this)

1. Do the experiment many times (each is a trial).
2. Count how many times the event happens (its frequency).
3. Divide by the number of trials.

Example: a drawing pin is dropped 120 times and lands point up 36 times. Estimate the probability that it lands point up.

1. Relative frequency = 36 ÷ 120
2. 0.3

The more trials you do, the closer the relative frequency usually gets to the true probability. A few trials can give a misleading result.

• A fair dice, coin or spinner has every outcome equally likely.
• A biased one doesn't.

To judge, compare the relative frequency (from lots of trials) with the probability you'd expect if it were fair.

Example: a dice is rolled 300 times, and a six comes up 85 times. Is it biased?

1. Relative frequency of a six: 85 ÷ 300 = 0.28…
2. For a fair dice: 1/6 = 0.17 (to 2 d.p.)
3. 0.28 is much higher, after 300 rolls, so the dice is probably biased towards six

With only 30 rolls, the same difference would be much less convincing.

To predict how many times an event will happen:

Expected number = probability × number of trials (learn this)

Example: the probability a spinner lands on red is 0.15. It is spun 200 times. How many reds would you expect?

1. 0.15 × 200 = 30 reds

Example: the drawing pin from before lands point up with relative frequency 0.3. How many times would you expect it to land point up in 500 drops?

1. 0.3 × 500 = 150 times