//  File MIT-Lab-02-01-00-01.txt. Edition 2/26/2020.

//  Lab Specs
//     Title
         Card_Draw_-_Relative_Frequency

//  Problem Specs
//    PauseCheckbox(-1 checked 0 cleared)


` -1
Objective: Illustrate the relative frequency interpretation of probability.
 That is, show that after many, many repetitions of the experiment, the
 distribution of the random variable's numerical values mirrors the
 probability distribution of the random variable.
_
Scroll down the list of cards and select four to be in the deck: 2 of Clubs,
 3 of Hearts, 3 of Diamonds, and 4 of Hearts.
` -1
Experiment: Draw one card from a deck and then replace it.
_
The list in the upper left corner of the window indicates the cards that are
 in the deck. Be certain that the 2 of Clubs, 3 of Hearts, 3 of Diamonds,
 and 4 of Hearts are selected.
_
Let v equal the "value" of the card drawn; that is, v equals 2 if the 2 of Clubs is drawn,
 3 if the 3 of Hearts or the 3 of Diamonds is drawn, and 4 if the 4 of Hearts is drawn.

` -1
1. What is the probability that v would equal each of its possible
 values (2, 3, and 4) for a single repetition the experiment?
_
Note that the Pause checkbox is checked. Consequently, the simulation will pause 
 after each repetition.
_
2. Click the Start button. Which card was drawn from the deck? What does numerical value
 of v equal on the first repetition of the experiment?

` -1
3. Click the Next button to repeat the experiment for a second time. 
 What does numerical value of v equal on the second repetition of the experiment?
 Click the Next button a few more times. What does the numerical value of v equal
 for each repetition of the experiment? Explain why v is a random variable.
_
The histogram seen above illustrates the distribution of the numerical values of the v's visually;

` 0
Now the Pause checkbox has been cleared. Therefore, the simulation will no longer
 pause after each repetition of the experiment.
_
4. Click the Next button. 
 After many, many repetitions click the Stop button. What are the relative 
 frequencies of the numerical values of the v's after many, many repetitions?
_
5. Compare your answers to 1 and 4; that is, compare the probabilities and
 the relative frequencies. How is the probability distribution related to the
 distribution of the numerical values after many, many repetitions?