Binomial probability
This presentation is the property of its rightful owner.
Sponsored Links
1 / 9

Binomial Probability PowerPoint PPT Presentation


  • 37 Views
  • Uploaded on
  • Presentation posted in: General

Binomial Probability. To be considered to be a binomial experiment Fixed number of trials denoted by n n trials are independent and performed under identical conditions Each trial has only two outcomes: success denoted by S and failure denoted by F

Download Presentation

Binomial Probability

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Binomial probability

Binomial Probability

To be considered to be a binomial experiment

Fixed number of trials denoted by n

n trials are independent and performed under identical conditions

Each trial has only two outcomes: success denoted by S and failure denoted by F

For each trial the probability of success is the same and denoted by p. The probability of failure is denote by q and p+q=1 (or q = 1 - p)

The central problem is to determine the probability of r successes out of n trials. P(r) =


Understanding the concept

Understanding the Concept

  • If the doctor tells you that the success rate for a given operation is 50%. That means that any given time the operation is performed there is a 50% chance of success.

  • If the doctor performs 3 of these operations in a single day, the probability that all thee will be successful is 12.5%, it is also true that there is a 37.5% chance that 1 of the three will be successful.

  • Where do these percentages come from?

    • This is the discussion of the presentation


Finding the p x successes

Finding the P( x successes)

  • There are several ways one can approach this problem

    • Calculating it by hand

    • Using a Binomial distribution table

    • Using technology


Basic example

BASIC EXAMPLE

  • Given 5 trials, with an historical probability of success on A SINGLE TRIAL of 25% .

    Of the 5 trials

  • You can find the P(0 successes), P(1 success), P(2 successes) , P(3 successes), P(4 successes), or P(5 successes).

  • As an example, the following calculation will be for P(4 successes)


By hand p 4 successes

BY HAND P( 4 successes)

  • If n = 5 (number of trials) and p = 0.25, what is the probability of 4 successes let (x = 4)?

  • P(4) = ?

  • p + q = 1 so q = 1 – r = 1 – 0.25 = 0.75

    Using the Formula on page 426 of text

  • P(x) = Cn,x times px times qn-x

  • P(4) = C5,4 0.254 0.755-4

  • P(4) = 5 * 0.254 0.751

  • P(4) = 5 * 0.0039 * 0.75 = 0.014625 ≈ 0.0146


By table p 4 successes

By Table: P( 4 successes)

By Using Binomial Probability table such as found at : http://www.uwsp.edu/math/hgonchig/Math_355/Tables/Binomial.pdf

-P( 4 successes)

  • n=5, x=4, P(x) = 0.25

  • P(4) = .0146

http://www.uwsp.edu/math/hgonchig/Math_355/Tables/Binomial.pdf


By technology p 4 successes

By Technology: P( 4 successes)

Excel = BIOMDIST(4,5,0.25,false) Ans: .0.014648438

TI 83 – 84

2nd DISTR choice 0 ENTER binompdf ( 5,0.25,4) ENTER Ans: 0.14648375

IF YOU USE ONE OF THESE TWO METHOD, EITHER ATTACHED THE EXCEL WORKBOOK, OR IF USING THE TI 83 OR 84 STATE THE FUNCTION AND ITS PARAMETERS.


The entire probability distribution

The Entire Probability Distribution

  • Given 5 trials, with an historical probability of success on A SINGLE TRIAL of 25%

  • P(of 0 success out of 5 trials) = .2373

  • P(of 1 success out of 5 trials) = .3955

  • P(of 2 successes out of 5 trials) = .2637

  • P(of 3 successes out of 5 trials) = .0879

  • P(of 4 successes out of 5 trials) = .0146

  • P(of 5 successes out of 5 trials) = .0010


Summary

Summary

  • You should be able to calculate a binomial probability by any of the three methods.

  • Questions: post the slide number and your question to your individual forum.


  • Login