# SOCR EduMaterials Activities DieCoinExperiment

## Description

The die coin experiment consists of rolling a die and then tossing a coin the number of times shown on the die. The die score X and the number of heads Y are recorded on each update. The density function and moments of Y are shown in blue in the second graph and are recorded in the second table. On each update, the empirical density and moments of Y are shown in red in the second graph and are recorded in the second table. The probability of heads for the coin can be varied with the scroll bar. You can specify the die distribution by clicking on the die probability button; this button brings up the die probability dialog box.

You can define your own distribution by typing probabilities into the text fields of the dialog box, or you can click on one of the buttons in the dialog box to specify one of the following special distributions: Fair 1-6 flat 2-5 flat 3-4 flat skewed left skewed right

## Goal

To provide a simulation of conditional probabilities with distribution tables and graphs. It allows the user to grasp the basic concepts of conditional events without computing numbers with the formula: $P(D3 | 2H) = {P(2H | D3) P(D3) \over P(2H)}$.

## Experiment

Go to the SOCR Experiment and select the Die Coin Experiment from the drop-down list of experiments on the top left. The image below shows the initial view of this experiment:

When pressing the play button, one trial will be executed and recorded in the distribution table below. The fast forward button symbolizes the nth number of trials to be executed each time. The stop button ceases any activity and is helpful when the experimenter chooses “continuous,” indicating an infinite number of events. The fourth button will reset the entire experiment, deleting all previous information and data collected. The “update” scroll indicates nth number of trials (1, 10, 100, or 1000) performed when selecting the fast forward button and the “stop” scroll indicates the maximum number of trials in the experiment.

As the number of trials increase, the empirical density and moments graph converge to the distribution graph (blue). The image below shows this property:

Note that when p decreases, the distribution graph becomes skewed right. When p increases, the distribution graph becomes uniform with the exception of a small value for 0. The image below demonstrates this outcome when p contains a high value:

## Applications

The Dice Coin Experiment is an applet that generalizes the important of experiments involving conditional probabilities. It allows users to understand the different outcomes when drawing the selected random variables with a varying probability.

This applet may also be used in place of other activities that occur in daily lives:

Suppose a gambler wants to test his chances of winnings in a casino given that he has already played a few successful games. Using this applet, the lets p be the probability of his current winnings and runs the experiment several times to graphically display his next chances of winning again.

Suppose researchers want to be able to illustrate the probability of college students who take the bus with the conditional probability that they already have their driver’s license.