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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