## Wednesday, June 03, 2009

### Probability Distributions for Business Events - Binomial

System engineers and technical managers need to make decisions based on the probability of certain events occurring. For example during a risk assessment practice, the systems engineering might be calculating the risk value of an event, and based on the value of the risk level the organization will take certain steps to respond to the risk.

To accurately calculate the risk value which is calculated as the (impact level * probability of occurrence), the probability distribution selected needs to be accurate.

In some events outcomes could be binary, for example: good or bad, correct or incorrect, successful or failed, conforming or non-conforming. A suitable probability distribution would be a binomial probability distribution, using a binomial calculator the system engineer can calculate the probability of occurrence of one of the two possible events knowing the sample size (n), the rate of good versus bad, or correct versus incorrect (p) and the number of items (x) fitting a particular outcome. For example if we select a sample of six items from a batch which has a defect rate of 3%, we can find the probability that the sample has one defective item using the binomial formula

P(x) = [n! / x! (n-x)! ] p^x (1-p)^(n-x)

In the above example, n=6, p=0.03, x=1

Using the formula above or the binomial calculator available at Texas A&M, we get that P(1) = 0.1546

Stay tuned for other probability distributions that are also common in business environments.