How to Work a Binomial Distribution Formula

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Binomial distributions calculate the odds of success of an incident.
Binomial distributions calculate the odds of success of an incident. (Image: Creatas/Creatas/Getty Images)

Statisticians use the binomial distribution formula to compute the probability of success of a particular incident. Every incident can either be a success or a failure. This formula calculates the odds of success of the incident. Statisticians use the binomial distribution formula in a small sample size. The entire population is represented by “N” and the sample is represented by “n.” The binomial distribution formula is used as a good estimation. There are few steps involved in the computation.

Understand the problem carefully. For example, the problem may ask you to compute the probability of customers buying a particular color of a product. The company may the produce the product in two colors and 70% of the customers may prefer one color over the other. The problem may ask you calculate the probability of sale of a particular color product from a sample size.

Determine what you are required to calculate. The variable is denoted by “X”. In the same example, you may be required to calculate the number of people preferring a particular color from a sample size. Figure out your "N" (entire population), "n" (sample size), "X" (the variable for calculation) and “r” (number of trials.)

Convert the binomial variable into percentage form. Express the same problem in percentages. 70 percent of the population would prefer color 1 and 30 percent would prefer the second color.

Input figures into this formula : P(X = r) = nCr p r (1-p)n-r. With this, you would know the odds of a particular number of individuals preferring color 1 over color 2. If you wish to determine the odds for color 2, subtract the success rate of color 1 from 1.

Tips & Warnings

  • Please note that the summation of success rates for both the colors should always equal one. If the odds for success of color one are 0.639; the success rate for color 2 would be 0.361. That is 1- 0.639 = 0.361.

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