## Geometric Probability Model

**Overview:**

A geometric model is a probability model that tells us the probability of seeing our first success on the “xth” trial.

**Conditions:**

To be a geometric model, there can only be two possible outcomes: Success and Failure. Additionally, all trials must be independent from one another. Another requirement of a binomial model is that, throughout all trials, the probability of success remains the same.

**Using geometpdf (Probability of success, x-value):**

Use geometpdf when you need to find the probability of seeing your first success on

*the “xth” trial.*

**exactly****Using geometcdf (Probability of success, x-value):**

Use geometpdf when you need to find the probability of seeing your first success

**the “xth” trial.**

*on or before***Example 1:**

You roll a die 20 times. What is the probability that you roll your first 6 on the third trial?

1. First, define success: Each time I roll a 6.

2. Second, define the probability of success: (1/6)

3. Third, go to the geometpdf function on your calculator. This can be found under DISTR (2nd VARS)

4. Fourth, Enter the appropriate information in the calculator: geometpdf(1/6, 3) and hit enter.

5. The answer you get is 0.1157, which is the probability of rolling a 6, on the third trial.

**Example 2:**

You roll a die 30 times. What is the probability that you roll a 6 on or before the fifth trial?

1. First, define success: Each time I roll a 6.

2. Second, define the probability of success: (1/6)

3. Third, go to the geometcdf function on your calculator. This can be found under DISTR (2nd VARS)

4. Fourth, Enter the appropriate information in the calculator: geometcdf(1/6, 5) and press enter.

5. The answer you get is 0.5981, which is the probability of rolling a 6, on or before the fifth trial.