Joe Schumueller teaches a way of dealing with conditional probability called Bayesian Probability. It’s based on a theorem for finding the conditional probability that A occurs given that B has occurred if you know the probability that B occurs given that A has occurred, along with some additional probabilities.

- [Voiceover] Let's explore a special way, of dealing with conditional probability. It's called Bayesian Probability, and it's based on a theorem of refining the probability of A given B, if you know the probability of B given A, and some other probabilities. This is Baye's Theorem. The probability of A given B, is equal to the probability of B given A, times the probability of A, divided by the probability of B given A, times the probability of A, plus the probability of B given not A, times the probability of not A.

That's what those bars represent, not. How do we apply this? Here's an example. A multinational corporation gathers data on a new aptitude test for hiring applicants for trainee positions. They start by hiring all the applicants and giving them the test. They find that 70% of the applicants are successful in the position. Of the successful applicants, 90% passed the test. Of the unsuccessful applicants, 40% passed the test.

So, what the corporation wants to know is, what is probability of a applicant who passed the test, being successful in the position? This is an important question, if the corporation decides to only hire applicants, who successfully pass the test. So, let's set it up. A will equal successful applicant. An applicant who's successful in a position. B is an applicant who passes the test. So what we're looking for, is the probability of A given B.

The probability that applicant is successful, given that they've passed the test. Now, from the given information, what we know is that the probability, that an applicant is successful in the position is .70. We'll call that the probability of A. What this tells us, is the probability that the applicant is not successful, is .30. That's the probability of not A. Notice that .70 and .30, the probability of A and the probability of not A, add up to 1.00, more given information.

The probability that the applicant passed the test, given that the applicant is successful is .90. That's the probability of B given A. What this tells us, is that the probability that the applicant did not pass the test, given that the applicant is successful is .10. That's the probability of not B, given A. Notice that they add up to 1.00 also. And, the probability that the applicant passed the test, given that the applicant is not successful is .40. That's the probability of B given not A.

That tells us, that the probability that the applicant did not pass the test, given that the applicant is not successful is .60. And that's the probability of not B, given not A. So, all that combines together in Baye's Theorem in this way. The probability of B given A, times the probability of A, divided by the probability of B given A, times of probability of A, plus the probability of B, given not A, times the probability of not A.

In plugging in all the numbers that we have, and the numbers that we're able to figure out, it's .90, times .70, divided by .90, times .70, plus .40 times .30, which is equal to .84, for the probability of A given B. And this is a direct application of Baye's Theorem.

###### Updated

7/6/2016###### Released

1/31/2016He explains how to organize and present data and how to draw conclusions from data using Excel's functions, calculations, and charts, as well as the free and powerful Excel Analysis ToolPak. The objective is for the learner to fully understand and apply statistical concepts—not to just blindly use a specific statistical test for a particular type of data set. Joseph uses Excel as a teaching tool to illustrate the concepts and increase understanding, but all you need is a basic understanding of algebra to follow along.

- Identify functions and charts available for use in Excel.
- Recognize the definition of the Bayesian probability.
- List the three measures of central tendency.
- Compare the usage of inferential statistics to the usage of standard normal distribution.
- Calculate the confidence level when provided the alpha level of uncertainty.
- Define a Type I and Type II error of hypothesis testing.
- Explain when to use a z-test or a t-test.
- Recall the types of variance that occur in multi-factored studies.
- Summarize the function of variables in multiple regression.
- Name three types of correlation values.

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Video: Bayesian probability