Welcome to module six.

Most people have an intuitive sense of probability.

We encounter it often, either in a weather forecast where

the likelihood or probability of precipitation is stated,

and sporting events like horse racing where

the odds or relative probabilities of winning are stated,

or in business where forecasts are determined

from all available data to make predictive decisions.

While these terms may be used frequently,

do you really have a solid grasp from them?

For example, what does it really mean to have a 40% likelihood of rain?

Or that one horse has odds of five to one,

while another has odds of thirteen to two?

Or what is the likelihood a batter gets a hit when its average is 300?

In this module, we will explore these concepts,

starting with the basic concepts of probability before discussing more complex issues.

Throughout, we will resort to simple demonstrations often based on flipping a coin,

rolling a dice, or drawing a card from a deck.

In this manner, you should develop a solid understanding of this important topic.

First, you will read about the basic concepts in probability,

including how to compute a probability,

the concept of discrete and continuous random variables,

modeling a random process by using a theoretical distribution,

and representing experimental data with empirical distributions.

These topics will help you understand how to compute probabilities for simple events,

and to incorporate probabilities into your decision-making.

Second, you will read about more advanced concepts in

probability including the notion of independence,

which indicates whether events are somehow tied together,

like the probability of rain if the sky is cloudy,

before moving on to conditional probability where

we will calculate the probability it might rain given the sky is cloudy.

Finally, Bayes theorem is introduced,

which is an important theoretical result that allows

the computation of the probability of a hypothesis given

the observed data from the product of the likelihood of the data given

the hypothesis and the prior probability of the hypothesis.

I realize that might sound a little confusing,

but it will make more sense after this module.

These topics are helpful when facing more complicated questions such as,

what is the likelihood of rain on a days after it has already rained?

What is the probability a batter will get a hit against the left handed pitcher?

Or how likely will it be that a company's sales will

decrease when bad weather impacts their supply chain?

Finally, the last two lessons will put these concepts into practice by using Python.

First, you will learn how to compute probabilities,

how to build empirical probability distributions from observed data,

and how to use these empirical distributions to make future decisions.

Second, you will learn about some of the more important theoretical distributions,

such as the Poisson and normal distributions,

and how they can be used to model random processes.

While they might seem simple or even dry,

these ideas are fundamental to analyzing data or building models to describe your data.

I encourage you to carefully read and try out all of

the examples in this module and to think deeply about these topics.

Try to apply them in your everyday life whether it be analyzing the weather report,

watching sporting events, or modeling and incorporating probabilities in your daily life.

Your investment now will be rewarded later. Good luck.