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Simulating Probability Situations Using Box Models
The interactive tool in this i-Math investigation is
a "box model" that allows students to explore
the relationship between theoretical and experimental
probabilities. A "box model" is a statistical
device that can be used to simulate standard probability
experiments such as flipping a coin or rolling a die.
To use the "box model":
- To Enter Data: Click on the number pad to enter numbered
tickets into the box.
- To Randomly Draw Tickets: Click on the Start button
to randomly draw tickets from this box (with replacement)
and view, in real time, the experimental probability
of drawing a given ticket.
- To Pause the Drawing: When you press the Pause button
the "box model" pauses drawing. You can then
click on any bar in the bar chart to display the current
relative frequency.
- In pause mode, you are also able to scroll through
the sample of the numbers drawn thus far.
Sample Activity: Flipping a Coin
- Click on the 0 and the 1 to move them into the "box
model."
- Click the "Show Theoretical Probability"
checkbox to see the theoretical probability values displayed
on the bar chart.
- Read the bar chart to answer the following questions:
What is the theoretical probability for heads? For tails?
- Click on the Start button. (This begins a random draw,
with replacement).
- Click on the Start button to pause the drawing after
10 draws.
- After 10 draws, what is the experimental probability
of heads? Of tails? Why is this different from the theoretical
probability?
- Begin the drawing again by pressing Start. Pause after
20 draws.
- Is the experimental probability closer to the theoretical
probability than after 10 draws? Explain why more draws
affects the closeness of the two values.
- Predict the number of draws that would bring the values
"very" close to each other.
- Test your conjecture by beginning the drawing again
and pausing after you reach your predicted number of
draws. Repeat if necessary until you have gotten the
two values "very" close to each other.
- What hypothesis can you make at this point about the
number of draws it would take to insure that the experimental
and theoretical probabilities are equal?
The box model below allows you to replicate
the drawing of many numbers and then investigate the distribution
of the sum of draws or average of draws. Try it. Describe
and explain any patterns you see.
References and Credits
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