Introduction to Probability Activity Statistics
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Probability is the proportion of times a certain result happens in a very large set of results.
We record theoretical probability like this:
The Number of Ways Event A Can Oc cur
P( A)=Probability Event A will Occur=
¿ tal Number of Possible Outcomes .
The Monty Hall problem is named as such because of its similarity to the Let's Make a Deal television
game show hosted by Monty Hall. Here is the problem. Suppose that a room is equipped with three
doors. Behind two are goats, and behind the third is a shiny new car. You choose a door and then you win
whatever is behind it.
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However, before the door you chose is opened, the game show host, Monty Hall, opens one of the other
two doors, revealing a goat. Then, he asks you if you wish to change your selection to the third door (i.e.,
the door which neither you picked nor he opened). The problem is deciding whether you stay with your
original door or switch to the other one.
How many possible outcomes are there? 3 possible outcomes - one for each door
How many ways can you win the car? Just 1
What is the theoretical probability you win the car?
1
P ( car )= =0.333∨33.3 %
3
How many ways can you win a goat? 2
What is the theoretical probability you win a goat?
1
, Introduction to Probability Activity Statistics
2
P ( dog ) = =¿=0.667 or 66.7%
3
Stay Strategy: Use this link to play at least 15 rounds of the Monty Hall Game using the stay strategy.
Copy and paste your results here:
What is the probability you win the car with the stay strategy after 15 rounds?
1
P(car)= =0.2 or 20.0%
5
What is the probability you win a goat with the stay strategy after 15 rounds?
4
P(goat¿= =0.8 or 80.0%
5
These results are experimental probabilities. Experimental probability is based on data collected during
an investigation or experiment.
Now, click Reset and change the screen so that it looks like this:
● Uncheck the Animate box
● Repeat the stay strategy 100 times.
● Hit the Go button.
● Watch the Cumulative Wins
Proportion graph.
● Repeat hitting the Go button until
you have 1000 rounds.
2
Image found at this web address
Probability is the proportion of times a certain result happens in a very large set of results.
We record theoretical probability like this:
The Number of Ways Event A Can Oc cur
P( A)=Probability Event A will Occur=
¿ tal Number of Possible Outcomes .
The Monty Hall problem is named as such because of its similarity to the Let's Make a Deal television
game show hosted by Monty Hall. Here is the problem. Suppose that a room is equipped with three
doors. Behind two are goats, and behind the third is a shiny new car. You choose a door and then you win
whatever is behind it.
Image found at this web address
However, before the door you chose is opened, the game show host, Monty Hall, opens one of the other
two doors, revealing a goat. Then, he asks you if you wish to change your selection to the third door (i.e.,
the door which neither you picked nor he opened). The problem is deciding whether you stay with your
original door or switch to the other one.
How many possible outcomes are there? 3 possible outcomes - one for each door
How many ways can you win the car? Just 1
What is the theoretical probability you win the car?
1
P ( car )= =0.333∨33.3 %
3
How many ways can you win a goat? 2
What is the theoretical probability you win a goat?
1
, Introduction to Probability Activity Statistics
2
P ( dog ) = =¿=0.667 or 66.7%
3
Stay Strategy: Use this link to play at least 15 rounds of the Monty Hall Game using the stay strategy.
Copy and paste your results here:
What is the probability you win the car with the stay strategy after 15 rounds?
1
P(car)= =0.2 or 20.0%
5
What is the probability you win a goat with the stay strategy after 15 rounds?
4
P(goat¿= =0.8 or 80.0%
5
These results are experimental probabilities. Experimental probability is based on data collected during
an investigation or experiment.
Now, click Reset and change the screen so that it looks like this:
● Uncheck the Animate box
● Repeat the stay strategy 100 times.
● Hit the Go button.
● Watch the Cumulative Wins
Proportion graph.
● Repeat hitting the Go button until
you have 1000 rounds.
2
