# BinomialDist Command

From GeoGebra Manual

- BinomialDist( <Number of Trials>, <Probability of Success> )
- Returns a bar graph of a Binomial distribution.
- The parameter
*Number of Trials*specifies the number of independent Bernoulli trials and the parameter*Probability of Success*specifies the probability of success in one trial. **Note:****BinomialDist( <Number of Trials>, <Probability of Success>,<List of values>)**is also available.- BinomialDist( <Number of Trials>, <Probability of Success>, <Boolean Cumulative> )
- Returns a bar graph of a Binomial distribution when
*Cumulative*= false. - Returns a graph of a cumulative Binomial distribution when
*Cumulative*= true. - First two parameters are same as above.
- BinomialDist( <Number of Trials>, <Probability of Success>, <Variable Value>, <Boolean Cumulative> )
- Let X be a Binomial random variable and let v be the variable value.
- Returns P( X =
*v*) when*Cumulative*= false. - Returns P( X ≤
*v*) when*Cumulative*= true. - First two parameters are same as above.
**Note:**A simplified syntax is available to calculate P(*u*≤ X ≤*v*): e.g.`BinomialDist(10, 0.2, 1..3)`

yields*0.77175*, that is the same as BinomialDist(10, 0.2, {1, 2, 3}). This syntax also works in the CAS View

## CAS Specific Syntax

In CAS View only one syntax is allowed:

- BinomialDist( <Number of Trials>, <Probability of Success>, <Variable Value>, <Boolean Cumulative> )
- Let X be a Binomial random variable and let v be the variable value.
- Returns P( X =
*v*) when*Cumulative*= false. - Returns P( X ≤
*v*) when*Cumulative*= true.

**Example:**You can plot a graph with eg`f(x):=BinomialDist(100,x,36,true)-BinomialDist(100,x,23,true)`

**Example:**Assume transfering three packets of data over a faulty line. The chance an arbitrary packet transfered over this line becomes corrupted is \frac{1}{10}, hence the propability of transfering an arbitrary packet successfully is \frac{9}{10}.`BinomialDist(3, 0.9, 0, false)`

yields*\frac{1}{1000}*, the probability of none of the three packets being transferred successfully.`BinomialDist(3, 0.9, 1, false)`

yields*\frac{27}{1000}*, the probability of exactly one of three packets being transferred successfully.`BinomialDist(3, 0.9, 2, false)`

yields*\frac{243}{1000}*, the probability of exactly two of three packets being transferred successfully.`BinomialDist(3, 0.9, 3, false)`

yields*\frac{729}{1000}*, the probability of all three packets being transferred successfully.`BinomialDist(3, 0.9, 0, true)`

yields*\frac{1}{1000}*, the probability of none of the three packets being transferred successfully.`BinomialDist(3, 0.9, 1, true)`

yields*\frac{7}{250}*, the probability of at most one of three packets being transferred successfully.`BinomialDist(3, 0.9, 2, true)`

yields*\frac{271}{1000}*, the probability of at most two of three packets being transferred successfully.`BinomialDist(3, 0.9, 3, true)`

yields*1*, the probability of at most three of three packets being transferred successfully.`BinomialDist(3, 0.9, 4, false)`

yields*0*, the probability of exactly four of three packets being transferred successfully.`BinomialDist(3, 0.9, 4, true)`

yields*1*, the probability of at most four of three packets being transferred successfully.