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Long-run experiments
The more times a probability experiment is done, the more
accurate the experimental probability (or relative frequency) is.
An experiment is done 1000 times and the relative
frequencies are plotted after every 100 attempts. Which
of these is the most likely graph and why?
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A Monte Carlo method
Look at this diagram and imagine picking
a random spot within the square:
What would be the probability
that the point was inside the
orange circle?
What would the relative
frequency tend to if we
repeated the experiment?
We can find an estimate of π using probability!
This is called a “Monte Carlo” method.
Some computers use Monte Carlo methods for doing
complicated calculations.
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Monty Hall problem
A game show host offers you one of three doors: behind one
door is a car, behind the others there are goats.
You pick a door, and the host, who knows what is behind the
doors, opens one of
the others to reveal
a goat.
He asks if you
would like to
change your
choice to the other
unopened door.
Should you?
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Monty Hall problem
Suppose you initially choose a door with a goat behind.
What is the probability of this?
If you initially choose a door with a goat behind, and
choose to stay, what prize will you receive?
If you choose to stay, the probability of
winning a goat is 2 . The probability of
3
1
winning a car is 1- P(goat) = .
3
If you initially choose a door with a
goat behind, and choose to change,
what prize will you receive?
If you choose to change, the probability
of winning a car is 2 .
3
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Monty Hall problem
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