Probability of Binomial Experiments.

What are the conditions to define a binomial experiment? How are the probabilities for a binomial experiment calculated? Why is called a binomial experiment? Is it related to the Binomial Theorem? What is the Binomial Theorem? By going through the lesson you will be able to realize that there is a set of conditions for a binomial experiment to be conducted that way. In order to deepen in this understanding the lesson presents for you the development of the binomial theorem proof. Once this has started, you may stop running it and then continue it by yourself using the pen from the pull down menu labeled as MARKER TOOLS menu. Then you may continue running the presentation to verify if you did it the right way. As always when studying a lesson, it is useful to go over the associated definitions. Some of them are given at the bottom of the page. Just scroll further down the page where the lesson is displayed.

This is a short but interesting lesson, that addresses the answers for all of the above questions. You will find it that is crystal clear, and easy to follow!

Lesson's Content

Lesson In PDF Format (no animations)

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Lesson's Glossary

Binomial Experiment: A experiment that has only two possible outcomes.

Binomial probability: Finds probabilities of binomial experiments and uses the binomial theorem to find the probabilities.

Binomial Theorem: If we expand (x + y)n and n is a positive integer then
(x + y)n=
C0xn + C1xn-1y1 + C2xn-2y2 + ... + Cn-1x1yn-1 + Cnyn

Combination: Any arrangement in which order is not important.

Dependent events: The outcome of a dependent event is affected by the outcome of the previous event.

Independent Events: If an outcome doesn’t affect the outcome of a following event, then the two events are independent.

Factorial! n! represents the product of all the whole numbers from n to 1. n! is the product of all the whole numbers from n down to 1 - used in probability.

Outcomes: The possible results of a probability experiment.

Pascal's Triangle: A pattern made in the shape of a pyramid finding the coefficients of the terms generated by a binomial expansion. It is used in probability as well.

Permutation: Any arrangement in which order is important.

Probability: The possibility of an event to happen. The probability of getting an even number when rolling a 6 sided dice is 50%.

Sample Space: All possible ways an event may happen.

 

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