Basic Probability Concepts

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From the course by University System of Georgia

Six Sigma Advanced Define and Measure Phases

180 ratings

University System of Georgia

Six Sigma Advanced Define and Measure Phases

180 ratings

Course 2 of 4 in the Specialization Six Sigma Green Belt

This course is for you if you are looking to dive deeper into Six Sigma or strengthen and expand your knowledge of the basic components of green belt level of Six Sigma and Lean. Six Sigma skills are widely sought by employers both nationally and internationally. These skills have been proven to help improve business processes and performance. This course will take you deeper into the principles and tools associated with the "Design" and "Measure" phases of the DMAIC structure of Six Sigma. It is highly recommended that you complete the "Yellow Belt Specialization" and the course "Six Sigma and the Organization (Advanced)" before beginning this course. In this course, your instructors will introduce you to, and have you apply, some of the tools and metrics that are critical components of Six Sigma. This course will provide you with the advanced knowledge of team dynamics and performance, process analysis, probability, statistics, statistical distributions, collecting and summarizing data, measurement systems analysis, process and performance capability, and exploratory data analysis associated with Six Sigma and Lean. Every module will include readings, videos, and quizzes to help make sure you understand the material and concepts that are studied. Registration includes online access to course content, projects, and resources but does not include the companion text The Certified Six Sigma Green Belt Handbook (2nd edition). The companion text is NOT required to complete the assignments. However, the text is a recognized handbook used by professionals in the field. Also, it is a highly-recommended text for those wishing to move forward in Six Sigma and eventually gain certification from professional agencies such as American Society for Quality (ASQ).

From the lesson

Probability and Statistics - pt1

In this module, you will learn how mutually-exclusive events and independent events relate to probability. You will also learn how to solve basic probability problems, including those that require the addition, multiplicative, and conditional rules of probability.

Basic Probability Concepts3:58

Mutually Exclusive & Independent Events4:06

Addition Rules for Probability3:13

Conditional Probability2:17

Multiplicative Rules2:44

Meet the Instructors

Christina Scherrer, PhD
Professor of Industrial Engineering
Department of Systems and Industrial Engineering
Gregory Wiles, PhD
Interim Chair and Assistant Professor
Department of Systems and Industrial Engineering
Bill Bailey, PhD
Assistant Professor of Industrial Engineering
Department of Systems and Industrial Engineering

Probability is how we measure the likelihood of something random occurring.

This can be based on what we are currently

observing or on historical knowledge or experience.

For example, when you hear that there is

an accident on the route you typically drive home from work,

you will think, "It will probably take me longer to get home today."

Or, if your favorite team is winning by 30 points at half-time,

you may think they will probably win the game.

Some probabilities can be expressed more precisely than that.

For example, the probability of flipping heads on a fair coin is one half or 50%.

In probability, an event is any collection of outcomes from a probability experiment.

That is, an event could be one outcome or a combination of outcomes.

We are typically interested in determining the probability of an event.

The sample space is the collection of all the possible outcomes.

Let's take a look at those terms as they relate to tossing a die.

If we toss a die, we will end up with a number between one and six.

Each of those numbers is a possible outcome,

so our possible outcomes are one,

two, three, four, five, and six.

When we take those six outcomes together,

we have the sample space.

That is, the sample space is the set of whole numbers between one and six.

Then, there are a lot of possible events you could calculate the probability of.

For example, rolling a three,

which is just one outcome,

or rolling an odd number,

which is the outcomes one, three,

and five, or rolling a number less than or equal to two.

I'm sure you can think of others.

There are many important rules of probability that we will learn in this module.

Our first rule is that all probabilities must be between zero and one.

Something that is guaranteed to happen has a probability of one,

for example, tossing a die and getting a number less than 10 has a probability of one.

Since the sample space of outcomes for rolling

a die only has the numbers one through six,

we must get a number less than 10.

Something that cannot happen has a probability of zero.

Tossing a die and getting a number greater than 10 has a probability of zero.

This rule may seem obvious now,

but it is an important rule to remember as you work on harder probability problems.

If you have finished your calculations and have an answer

that is negative or an answer that is greater than one,

it should signal to you that you have done something wrong.

Another rule is that probability only describes what happens in the long run.

Using the example of tossing a coin,

just because we know the probability of flipping heads is one half,

it does not mean that if you flip a coin a number of times,

you will get heads exactly half of the time.

Think about flipping a coin just two times.

It isn't at all unusual to get heads both times or in either time.

However, in the long run,

as we replicate the coin toss over and over,

we expect that what we observe will be close to the true probability.

If we flip a coin 1,000 times,

we would expect fairly close to 500 heads.

This is an application of the law of large numbers.

Our third rule is that the sum of probabilities of

all possible outcomes of an event is one.

With the coin, since the two possible outcomes are heads or tails,

adding the probability of those two outcomes together must equal one.

And a quick check of that roll shows that one half plus one half does equal one.

This leads right into our last rule for this video,

which is called the complement rule or complementation rule.

The complement rule says that the probability that event A will not

occur is equal to one minus the probability that the event A will occur.

For example, we know that the probability of rolling a six on a die is one sixth.

To calculate the probability of not rolling a six,

we could calculate one minus one sixth,

which equals five sixth.

In this simple example,

it doesn't save much time to apply the complement rule,

but there will be later examples in this course where it is a very helpful rule indeed.

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