Probabilities can be written as fractions, decimals or percentages on a scale from 0 to 1. Knowing basic facts about equally likely outcomes can help to solve more complicated problems.

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**Relative**frequency is an estimate of probability and is calculated from repeated trials of an experiment.

The theoretical probability of getting a head when you flip a coin is \(\frac{1}{2}\), but if a coin was actually flipped 100 times you may not get **exactly** 50 heads, although it should be close to this amount.

If a coin was flipped a hundred times, the amount of times a head actually did appear would be the relative frequency, so if there were 59 heads and 41 tails the relative frequency of flipping a head would be \(\frac{59}{100}\) (or 0.59 or 59%).

Relative frequency is used to estimate probability when theoretical probability cannot be used.

For example, when using a biased die, the probability of getting each number is no longer \(\frac{1}{6}\). To be able to assign a probability to each number, an experiment would need to be conducted. From the results of the trials, the relative frequency could be calculated.

The more trials in the experiment, the more reliable the relative frequency is as an estimate of the probability.

Ella rolls a biased die and records how many times she scores a six. Estimate the probability of scoring a six with Ella’s die.

Number of rolls (trials) | 10 | 20 | 30 | 40 | 50 |
---|---|---|---|---|---|

Total number of sixes | 2 | 3 | 6 | 8 | 9 |

Ella’s results will give different estimates of the probability, depending on the number of rolls of the die (the number of trials).

For example, after 10 rolls, the estimate for the probability of scoring a six is \(\frac{2}{10} = 0.2\), but after 20 rolls the estimate is \(\frac{3}{20} = 0.15\).

The most reliable estimate of the probability is found by using the highest number of rolls, which gives \(\frac{9}{50} = 0.18\).