BINOM.DIST Google Sheets

What Is BINOM.DIST Function in Google Sheets?

BINOM.DIST Google Sheets is used to calculate the probability of a specific number of successes when there are n independent Bernoulli trials. In other words, using the BINOM.DIST function, you can calculate the probability of obtaining a specified number of successes in a given number of trials. It follows the binomial distribution, where the word binomial refers to an event that has only two possible results: success or failure. It can calculate either the probability mass function or the cumulative distribution function depending on the value of the cumulative argument.

Let us look at a simple example of how to calculate the BINOM. DIST Google Sheets probability. To find the probability of 3 successes in 6 independent trials, where the success probability for each of the trials is 0.5, can be calculated as follows.

=BINOMDIST(3, 6, 0.5, FALSE)

The output of this formula gives the probability of precisely three successes in 6 trials based on the binomial distribution.

What Is BINOM.DIST Function in Google Sheets?

Binom.Dist Google Sheets is used to calculate the probability of attaining a fixed number of successes (or a maximum number) for a fixed number of n trials with a fixed probability of success.
The syntax of the BINOM.DIST function is
=BINOMDIST(num_successes, number_trials, probability_success, cumulative)
If the fourth argument cumulative is TRUE, BINOM.DIST returns the cumulative distribution function. This is the probability that there are a maximum number of successes. If it is FALSE, it returns the probability mass function, which is the probability of a fixed n number of successes.
We can use the BINOM.DIST under the following scenarios.
- For a fixed number of tests or trials
- When the outcome of any trial is only success or failure
- When the probability of success is fixed throughout

Syntax

The syntax of BINOM.DIST formula Google Sheets is as follows:

BINOM.DIST(k, n, p, cumulative)

k (required) is the number of successful outcomes for which you want to calculate the probability.
n (required) is the total number of independent trials or experiments.
p (required) is the probability of success of each trial. It should be between 0 and 1.
Cumulative (optional): This argument determines whether to calculate the cumulative probability up to the given number of successes. If it is TRUE or not mentioned, it calculates the cumulative probability. If FALSE, it calculates the probability of the exact number of successes.

How To Use Binom.Dist Function in Google Sheets?

The BINOMDIST function in Google Sheets calculates the probability of a given number of successes for a fixed number of trials. Let us look at how to use it with a suitable example.

Here, we are trying to find the probability of John getting heads exactly ten times when he tosses a coin 14 times. The success rate in this case is 0.5(he could get exactly heads or tails).

Step 1: Enter the data in your Google Sheets as follows. You can see the table below.

Step 2: To calculate the binomial distribution of this, apply the following function in cell B6.

Step 3: Press Enter. You get the value of the probability of exactly getting ten success in tossing the coin for 14 trials, which is 6.1% here.

From the Google Sheets Menu

Let us look at how to insert the function from the Google Sheets menu.

Step 1: First, go to the “Insert” option. GO to “Functions” and choose “Statistical.”

Step 2: Choose the BINOM.DIST function and enter the required arguments.

Examples

Let us look at some examples of how to calculate the binomial distribution under different everyday scenarios.

Example #1 – Probability of Getting Exactly 3 in 10 Dice Rolls

Dice rolls are commonly used in many games, and they have an outcome that can be precisely determined. Hence, in this example, let us calculate the probability of getting exactly 3 when a die is rolled ten times. The data within the provided table is organized as follows:

In this example, one roll of the dice is a trial. Here, the result of this calculation is the number of threes that were thrown in ten trials. When we throw a die, the probability of getting a three is exactly 1/6 in a trial. Hence, we have written 0.1666666 in cell B4.

Step 2: Apply the formula as follows in cell B5.

=BINOM.DIST(B2,B3,B4,FALSE)

FALSE represents the exact number of successes in obtaining 3 in 10 trials.

Step 3: Press Enter. You get the probability of the occurrences of throwing 3 in 10 trials (0.15504).

Example #2 – Cumulative Probability of 5 or Fewer Tails in 20 Coin Flips

Flipping a coin has two outcomes – success and failure. Here, let us calculate the cumulative probability of getting five or lower tails with the flip of a coin twenty times. Here, the probability of getting less than or equal to k successes requires us to apply TRUE as the fourth argument.

Let us enter the details in a Google sheet.

Step 1: Here, the probability of getting tails when you flip a coin is ½ or 0.5. Apply the following formula in cell B5.

Step 2: Press Enter. You get the cumulative probability of the event of getting tails 5 or lesser number of times when you flip a coin 20 times as follows:

The value is around 2%.

Example #3 – Probability of 4 or More Heads in 10 Coin Flips.

Now, that we have seen the scenarios of calculating the probability of exactly k number of successes, and less than or equal to k successes, let us check what is the probability of obtaining heads 4 or more times for 10 flips of a coin.

Like the above two examples, let us enter the details in a table. Here, we enter the number as 3 because we are calculating the probability of 3 or fewer heads in 10 flips and subtracting it from 1 to get the probability of 4 or more heads during a 10 coin flip.

Step 1: Include the following formula in cell B5.

=BINOM.DIST(B2,B3,B4,TRUE)

Step 2: Press Enter. You get the probability of less than or equal to 3 occurrences of heads in a 10 coin flip. Now, to get the probability of 4 or more occurrences of heads, subtract this value from 1. The answer is 0.828 or 82.8%.

Important Things to Note

If any of the parameters like number of successes, number of trials, and probability of success are non-numeric, you get a #VALUE! error.
You get an #NUM error if the number of trials is less than the number of successes or if the number of successes is a negative value.
You also get the #NUM error when the probability is not between zero and one.
The number of successes and trial parameters are always truncated to integers.

Frequently Asked Questions (FAQs)

What are the reasons for BINOM.DIST Google Sheets not working?

Below are some of the common reasons for errors when using the BINOM.DIST Google Sheets function.

1. One common mistake is misunderstanding the meaning of the parameters. For example, the first parameter refers to the number of successful trials and not the success probability.
2. Mentioning the wrong probability value is another reason. Ensure that you mention the probability of success for each trial.
3. Use the right cumulative parameter. Do not use TRUE in the place of false.
4. Last but not least, do not forget to include all the parameters.

What is the difference between BINOM.DIST and BINOM.INV in Google Sheets?

The BINOM.DIST function gives the probability of a particular number of successes in fixed trials with a probability of success in each trial as a parameter. We commonly use it in statistical analysis and hypothesis testing. The output of the function can either be the probability mass function or the cumulative distribution function (CDF), which depends on whether the fourth parameter is true or false. Its formula is BINOMDIST(number_successes, trials, probability, cumulative).

The BINOM.INV function calculates the least value for which the cumulative binomial distribution is lesser than or equal to a specified value. We use it to find the exact number of successes in a number of fixed independent trials which has a known success probability. Its formula is =BINOM.INV(trials, probability_s, alpha).

What are the uses of the BINOM.DIST Google Sheets function?

• BINOM.DIST Google sheets calculator calculates the probability of a binary occurrence. An example is the probability of heads when tossing a coin.
• It also calculates the probability of a certain number of successes occurring within a given time frame.
• It can find the probability of a particular number of successes in n number of trials.

BINOM.DIST Google Sheets