# How to Calculate Binomial Probabilities on a TI-84 Calculator

The binomial distribution is one of the most commonly used distributions in all of statistics. This tutorial explains how to use the following functions on a TI-84 calculator to find binomial probabilities:

binompdf(n, p, x) returns the probability associated with the binomial pdf.

binomcdf(n, p, x) returns the cumulative probability associated with the binomial cdf.

where:

• = number of trials
• = probability of success on a given trial
• = total number of successes

Both of these functions can be accessed on a TI-84 calculator by pressing 2nd and then pressing vars. This will take you to a DISTR screen where you can then use binompdf() and binomcdf():

The following examples illustrate how to use these functions to answer different questions.

### Example 1: Binomial probability of exactly x successes

Question: Nathan makes 60% of his free-throw attempts. If he shoots 12 free throws, what is the probability that he makes exactly 10?

Answer: Use the function binomialpdf(n, p, x):

binomialpdf(12, .60, 10) = 0.0639

### Example 2: Binomial probability of less than x successes

Question: Nathan makes 60% of his free-throw attempts. If he shoots 12 free throws, what is the probability that he makes less than 10?

Answer: Use the function binomialcdf(n, p, x-1):

binomialcdf(12, .60, 9) = 0.9166

### Example 3: Binomial probability of at most x successes

Question: Nathan makes 60% of his free-throw attempts. If he shoots 12 free throws, what is the probability that he makes at most 10?

Answer: Use the function binomialcdf(n, p, x):

binomialcdf(12, .60, 10) = 0.9804

### Example 4: Binomial probability of more than x successes

Question: Nathan makes 60% of his free-throw attempts. If he shoots 12 free throws, what is the probability that he makes more than 10?

Answer: Use the function 1 – binomialcdf(n, p, x):

1 – binomialcdf(12, .60, 10) = 0.0196

### Example 5: Binomial probability of at least x successes

Question: Nathan makes 60% of his free-throw attempts. If he shoots 12 free throws, what is the probability that he makes more than 10?

Answer: Use the function 1 – binomialcdf(n, p, x-1):

1 – binomialcdf(12, .60, 9) = 0.0834

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## 3 Replies to “How to Calculate Binomial Probabilities on a TI-84 Calculator”

1. abigail says:

Hi zach, your post has been extremely helpful to me. However, I’m curious what is the difference between question 4 and question 5.

2. RM says:

Great article

Example 5 question should read “… makes at least 10?”

3. Frederick Brown says:

Thank You, so much for making this clear. I am over here pulling out my hair and do not have none on my head.