The binomial distribution in statistics describes the probability of obtaining k successes in n trials when the probability of success in a single experiment is p.
To calculate binomial distribution probabilities in Google Sheets, we can use the BINOMDIST function, which uses the following basic syntax:
BINOMDIST(k, n, p, cumulative)
where:
- k: Number of successes
- n: Number of trials
- p: Probability of success on a given trial
- cumulative: Whether to calculate a cumulative probability (Default is FALSE)
The following examples show how to use this function in practice.
Example 1: Probability of Exactly k Successes
Ty makes 60% of his free-throw attempts. If he shoots 12 free throws, what is the probability that he makes exactly 10?
To answer this question, we can use the following formula in Google Sheets:
=BINOMDIST(10, 12, 0.6, FALSE)
The following screenshot shows how to use this formula in practice:
The probability that Ty makes exactly 10 free throw attempts out of 12 is 0.0639.
Example 2: Probability of Less Than k Successes
Ty makes 60% of his free-throw attempts. If he shoots 12 free throws, what is the probability that he makes less than 10?
To answer this question, we can use the following formula in Google Sheets:
=BINOMDIST(9, 12, 0.6, TRUE)
The following screenshot shows how to use this formula in practice:
The probability that Ty makes less than 10 free throw attempts out of 12 is 0.9166.
Example 3: Probability of Less Than Or Equal to k Successes
Ty makes 60% of his free-throw attempts. If he shoots 12 free throws, what is the probability that he makes less than or equal to 10?
To answer this question, we can use the following formula in Google Sheets:
=BINOMDIST(10, 12, 0.6, TRUE)
The following screenshot shows how to use this formula in practice:
The probability that Ty makes less than or equal to 10 free throw attempts out of 12 is 0.9166.
Example 4: Probability of Greater Than k Successes
Ty makes 60% of his free-throw attempts. If he shoots 12 free throws, what is the probability that he makes greater than 10?
To answer this question, we can use the following formula in Google Sheets:
=1-BINOMDIST(10, 12, 0.6, TRUE)
The following screenshot shows how to use this formula in practice:
The probability that Ty makes greater than 10 free throw attempts out of 12 is 0.0196.
Example 5: Probability of Greater Than or Equal to k Successes
Ty makes 60% of his free-throw attempts. If he shoots 12 free throws, what is the probability that he makes greater than or equal to 10?
To answer this question, we can use the following formula in Google Sheets:
=1-BINOMDIST(9, 12, 0.6, TRUE)
The following screenshot shows how to use this formula in practice:
The probability that Ty makes greater than or equal to 10 free throw attempts out of 12 is 0.0834.
Bonus: You can use the Binomial Distribution Calculator to automatically calculate binomial probabilities for any values for n, k, and p.
Additional Resources
The following tutorials provide additional information about the binomial distribution:
An Introduction to the Binomial Distribution
The Three Assumptions of the Binomial Distribution
5 Real-Life Examples of the Binomial Distribution
