# Probability:

# The Study of Randomness

We would first begin with a game called "**The
Spinning wheel**"

This will give the students a good idea of how to think about
**randomness**.

Introduce __the Law of Large Numbers__

*Draw independent observations at random
from any population with finite mean m. Decide how accurately
you would like to estimate m. As the number of observations
drawn increases, the mean x-bar of the observed values eventually
approaches the mean m of the population as closely as you specified
and then stays that close.*

Make a connection to the game. Have the students calculate
what the mean would be for that population, and let them discover
that as they take more and more trials that the mean will come
as close as they want.

### Basic Operations with Probabilities

Begin by defining what a **sample
space** and an **event**
is and moving into the **probability
of an event.**

Next we will move into discussing independence and basic operation
rules for computing event probabilities.

Follow by discussing the intersection, union and complement
of events.

## Descrete Random Variables

Begin by doing the classic **coin
toss experiment**.

Discuss the difinitions of a random variable and what it means
to be desrete (takes on numercial values) or continuous (values
that take on certain intervals).

Talk about Discrtete Probability Distributions and relate to
the game from the beginning.

Since this is a normal distribution make the connection to
Normal distributions (which resemble the bell shaped curves that
were discussed earlier in the semester.)

Move on to **The Binomial Distribution**
and the **Geometric Distribution.**

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