Relative Frequency

Relative Frequency

Relative Frequency

• This is the kind of probability that we determine from a survey or an experiment.

•Also known as experimental probability.

Relative Frequency

 $RF=\frac{number\ of\ successful\ trials}{total\ number\ of\ trials}=\frac{x}{N}$  

Example:

A football referee always uses a special coin. He notices that out of the last 20 matches the coin has come down heads far more often than tails. He wants to know if the coin is fair, that is, if it is as likely to come down heads as tails.

He decides to do a simple experiment by spinning the coin lots of times.

His results are shown in the table:

Observe this table properly before you go next page....

Multiple Choice

In the ‘long run’, that is after a large number of trials, did the coin appear to be fair?

• Yes

• No

Note:

The greater the number of trials the better the estimated probability or relative frequency is likely to be. The key idea is that increasing the number of trials gives a better estimate of the probability and the closer the result obtained by experiment will be to that obtained by calculation.

Example 1:

There is a group of 250 people in a hall. A girl calculates that the probability of randomly picking someone that she knows from the group is 0.032. Calculate the number of people in the group that the girl knows.

Example 2:

A boy enters 8 short stories into a writing competition. His father knows how many short stories have been entered into the competition, and tells his son that he has a probability of 0.016 of winning the first prize (assuming all the entries have an equal chance). How many short stories were entered into the competition?