Home Â» How to Calculate Binomial Probabilities on a TI-84 Calculator

# 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)Â returns the probability associated with the binomial pdf.

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

where:

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

Both of these functions can be accessed on a TI-84 calculator by pressingÂ 2ndÂ and then pressingÂ vars. This will take you to aÂ DISTRÂ screen where you can then useÂ binompdf()Â andÂ binomcdf():

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

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

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

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

binomialpdf(12, .60, 10) = 0.0639

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

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

binomialcdf(12, .60, 9) = 0.9166

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

Question:Â 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:Â Use the function binomialcdf(n, p, x):

binomialcdf(12, .60, 10) = 0.9804

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

Question:Â 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:Â Use the functionÂ 1 â€“ binomialcdf(n, p, x):

1 â€“ binomialcdf(12, .60, 10) = 0.0196

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

Question:Â 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:Â Use the functionÂ 1 â€“ binomialcdf(n, p, x-1):

1 â€“ binomialcdf(12, .60, 9) = 0.0834