## Binomial Probability Model

**Overview:**

A binomial model is a probability model with a fixed number of successes and a fixed number of trials.

**Conditions:**

To be a binomial 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 binompdf(number of trials, probability of success, number of successes)**

Use binompdf when you need to find probability of getting

*exactly*“x” many successes. Plug in the number of trials, followed by the probability of success, the number of successes (in order!!!).

**Using binomcdf(number of trials, probability of success, number of successes)**

Use binomcdf when you need to find the probability of getting “x”

**successes. Plug in the number of trials, followed by the probability of success, the number of successes (in order!!!).**

__or fewer__**Example 1**:

You roll a die 20 times; to see how many times you roll a 6. What is the probability that you roll a 6 three times?

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

2. Second, define the number of trials: 20

3. Third, define the probability of success: (1/6)

4. Fourth, go to the binompdf function on your calculator. This can be found under DISTR (2nd VARS)

5. Fifth, Enter the appropriate information in the calculator: binompdf(20, 1/6, 3) and press enter.

6. The answer you get 0.2379 is the probability of rolling a 6, three times, in 20 rolls.

**Example 2:**

You roll a die 30 times; to see how many times you roll a 6. What is the probability that you roll a 6 five times or less?

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

2. Second, define the number of trials: 30

3. Third, define the probability of success: (1/6)

4. Fourth, go to the binomcdf function on your calculator. This can be found under DISTR (2nd VARS)

5. Fifth, Enter the appropriate information in the calculator: binomcdf(30, 1/6, 5) and press enter.

6. The answer you get 0.6164 is the probability of rolling a 6, five times or less, in 30 rolls.