# 3.5 Geometric Probability Distribution using Excel Spreadsheet


How to use Excel function for Geometric

Suppose the probability that a red car enters an intersection is 0.24.  What is the likelihood that the first red car enters the intersection after four non-red vehicles pass through the intersection?  The discrete probability distribution is Geometric.

P(Red Car) = .24
P(Not Red Car) = 1-.24 = .76

P( X = 5) = (.76)4(.24) = 0.0801 Rounded to 4 decimal places

To compute the probability in an Excel spreadsheet, enter the formula below.

=NEGBINOM.DIST(4, 1, 0.24, FALSE)

• 4 represents the four non-red cars that have entered the intersection before the red car.
• 1 represents the first red car that enters the intersection.
• 0.24 is the probability of a red car entering the intersection.
• False means you want to compute a probability for one value, P(X = 5).
• True means you want to compute the P(X < 5).

The answer you should see is 0.080069.  Rounded to four decimal

You can also enter the following formula for one probability

= (.76^4)*.24

To make sure the formula is calculated, hit the Enter key after entering the formula.

Example $$\PageIndex{1}$$

Next, find the probability that at most 4 white cars pass through the intersection during one hour.

Solution

The probability statement is P(X < 4).  The Excel function is =NEGBINOM.DIST(3, 1, 0.24, True) .  The answer is 0.6664.

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