# Binomial Probabilities in Excel

Calculating binomial probabilities using a calculator can get very tedious very quickly.  This is especially true when calculating cumulative probabilities.  For example, suppose we are testing a sample of 50 parts (with replacement) where we expect an average defect rate of 1% and we want to know what the probability is of finding 2 or fewer defects in the batch.  This is a cumulative probability, so we have:

Which means we have to calculate:

which provides many chances to make errors.

Fortunately, we can use the Excel function BINOMDIST.  From the Insert menu, select Function, then select BINOMDIST from the statistical functions, which brings up the following window:

The entries are:

Number_s - the number of "successes" in the trial (2 in our problem)

Trials - the number of trials in our experiment (50 in our problem)

Probability_s - the probability of a success in a trial (0.01 in our problem)

Cumulative - Is the probability to be calculated cumulative (true in our problem) or not (false)

The BINOMDIST function can be entered directly.  For our problem we would enter:

=binomdist(2,50,0.01, true)