How do you calculate the relative frequency of a favourable outcome in 200 trials?

To calculate the relative frequency, divide the number of favourable outcomes by the total number of trials.

Relative frequency is a way to estimate the probability of an event occurring based on experimental data. In this case, you have conducted 200 trials. To find the relative frequency of a favourable outcome, you first need to count how many times the favourable outcome occurred during these trials. Let's call this number \( F \).

Once you have \( F \), the formula for relative frequency is:

\[ \text{Relative Frequency} = \frac{\text{Number of Favourable Outcomes}}{\text{Total Number of Trials}} \]

So, if you observed the favourable outcome 50 times out of 200 trials, you would calculate the relative frequency as follows:

\[ \text{Relative Frequency} = \frac{50}{200} = 0.25 \]

This means the relative frequency of the favourable outcome is 0.25, or 25%.

Relative frequency is useful because it gives you an empirical probability based on actual data, rather than theoretical probability, which is based on assumptions. It helps you understand how often an event is likely to occur in practice. For example, if you were rolling a die and wanted to know how often you roll a 4, you could roll the die 200 times and count how many times you get a 4. If you get a 4 on 30 of those rolls, the relative frequency would be:

\[ \text{Relative Frequency} = \frac{30}{200} = 0.15 \]

This tells you that, based on your trials, you can expect to roll a 4 about 15% of the time.