Relative Frequency

This page provides a simple example to illustrate the ideas behind relative frequency.

A Biased Coin

Suppose you have a coin which you know is biased towards Heads - this means the Heads has a greater chance of occurring.

However, you do now know what the probability of a HEAD occurring actually is.

Suppose you tossed the coin lots of times and go the following data

 Number of tosses 10 20 30 40 50 Number of heads 7 15 19 28 34 So, to tabulate this we can extend the table above:

 Number of tosses     60 Number of heads      Relative Frequency            As you can see, the probability seems to be around approaching a value of about 0.68 (to two decimal places).

A good estimate for To improve this estimate we would keep on increasing the total number of tosses.

We can draw a graph to show how our estimates appear to be approaching 0.68 Deductions from this and possible questions

·       P(heads)=0.68 THEREFORE P(tails)=0.32

·       If we tossed the coin 350 times (for example) we would expect ·       If we tossed the coin 3 times – we could find the probability of getting THREE HEADS

 Head and Head and Head Equals Answer       