What is the relative frequency if an event occurs 8 times out of 40 trials?

The relative frequency is 0.2 or 20%.

Relative frequency is a way of expressing how often an event occurs relative to the total number of trials or observations. To calculate the relative frequency, you divide the number of times the event occurs by the total number of trials. In this case, the event occurs 8 times out of 40 trials. So, you would calculate the relative frequency as follows:

\[ \text{Relative Frequency} = \frac{\text{Number of times the event occurs}}{\text{Total number of trials}} = \frac{8}{40} \]

When you divide 8 by 40, you get 0.2. This can also be expressed as a percentage by multiplying by 100, giving you 20%. Therefore, the relative frequency of the event occurring is 0.2 or 20%.

Understanding relative frequency is important because it helps you to analyse the likelihood of an event happening based on experimental or observed data. For example, if you were rolling a die and wanted to know how often you rolled a 3, you could use relative frequency to determine this. If you rolled the die 40 times and got a 3 on 8 of those rolls, the relative frequency would be 0.2, indicating that rolling a 3 is relatively common in your trials.

Relative frequency is particularly useful in situations where theoretical probability is difficult to calculate or when you want to compare experimental results with theoretical expectations. It provides a practical way to understand and interpret data in real-world scenarios.