## 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. fr(E) = the number of times E occurs Toss a coin 20 times. If heads comes up 13 times, then the frequency of the event that heads comes up is fr(E) = 13. The relative frequency or estimated probability of the event E is the fraction of times E occurs. P(E) = \frac{fr(E)}{N} 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 P(E) = \frac{fr(E)}{N} = \frac{13}{20} The number of times that the experiment is performed is called the sample size. N = number of times the experiment is performed. The experiment above was performed 20 times, so this is the sample size; N = 20.

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).

 The relative frequency that the sum is is P(E) = . Answer should be accurate to 4 decimal places.
Now think about the set of outcomes when we throw a pair of distinguishable dice such as these.
 . Answer should be accurate to 4 decimal places.

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 .
 N (Sample size) Sum (Red + Green) fr(E) (Frequency) P(E) (relative frequency) Answer should be accurate to 4 decimal places.

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.*

The relative frequency that a fast food outlet that specializes in Mexican food is is:

 P(E) = Answer should be accurate to 4 decimal places.

The relative frequency that a fast food outlet that specializes in Mexican food is is:

 P(E) = Answer should be accurate to 4 decimal places.

* 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
If 10 rolls of a die resulted in the outcomes 2, 1, 4, 4, 5, 6, 1, 2, 2, 1, then the associated relative frequency distribution is the one shown in the following table.

 Outcome s 1 2 3 4 5 6 Frequency fr(s) 3 3 0 2 1 1 Relative Frequency P(s) 0.3 0.3 0 0.2 0.1 0.1

You run a commercial website that specializes in the sale of video games. The following statistics show the number of downloads of your five on-line video games last week.

Fill in the following relative frequency table and press "Check."

 Outcome Dragon Quest Star Pilot Galactic Warrior 4 Detective III Advanced Star Pilot Relative Frequency