7.2: Relative Frequency (Estimated Probability) Game Version
To start, here are some basic definitions.
Definition  Example 
The frequency of the event E is the number of times the event E occurs.

Toss a coin 20 times. If heads comes up 13 times, then the frequency of the event that heads comes up is

The relative frequency or estimated probability of the event E is the fraction of times E occurs.
Note: It follows that P(E) must be a number between 0 and 1 (inclusive). 
Referring to the situation above, the relative frequency of the event that heads comes up is

The number of times that the experiment is performed is called the sample size.

The experiment above was performed 20 times, so this is the sample size;

Note: If E happens to consist of a single outcome s, then we refer to P(E) as the relative frequency of the outcome s, and we write P(s).
Now think about the set of outcomes when we throw a pair of distinguishable dice such as these.You will see in the next tutorial that, when the outcomes are all equally likely (as they are here) then the fraction of outcomes that are in E is the modeled probability of E.
Dice Simulation To simulate the above experiment, press the various "Throw Dice" buttons until you have simulated at least 100 throws of the dice. Then compute the relative frequency of the event E that the sum is . 
In 1993, there were approximately 10,000 fast food outlets in the US that specialized in Mexican food. Of these, the largest were Taco Bell with outlets, Taco John's with outlets and Del Taco with outlets.*
* Figures are slightly randomized for this tutorial but accurate to within 10 outlets. Source: Technomic Inc./The New York Times, February 9, 1995, p. D4.
You can find more examples similar to those above in Section 7.2 of and .
Relative Frequency Distribution
The collection of the relative frequencies of all the outcomes is the relative frequency distribution or estimated probability distribution. Example

Following are some of the properties of relative frequency. Which one did you use in answering the last question?
Some Properties of Relative Frequency
Let S = \{\.s_1, s_2, ..., s_n\.\} be a sample space and let P(s_i) be the estimated probability of the event \{s_i\}. Then
(a) 0 &le P(s_i) ≤ 1
In words:

For more practice, try some of the questions in the chapter review exercises (Warning: it covers the whole of Chapter 7). Also try the exercises dealing with relative frequency in Section 7.2 of and .