In mathematics, we are very familiar with the term** empirical probability**. We use it to count the occurrence of certain events with a simple formula. The **empirical probability formula** is widely used in business forecasting. In **Excel**, we can easily calculate empirical probability with a formula. Therefore, in this article, we will guide you on how to **calculate empirical probability** with the formula in excel discussing 4 examples.

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## What Is Empirical Probability Formula?

The **empirical probability formula **refers to the ratio of the number of outcomes to the total experiments performed. It shows the result of a particular event happening based on a certain number of trials, not on pre-conceived ideas.

It is mostly conceived in the business sector to determine profit and loss for a newly introduced product. Even in the government sector, we use the empirical probability formula to predict public acceptance of new policies.

The formula for empirical probability is given below:

**Empirical Probability = Number of outcomes / Number of Trials**

## Theoretical vs. Empirical Probability

As we know the **empirical probability** now, let us dive into the difference between **theoretical** and** empirical probability**. Before that, we need to know the** theoretical probability**. It is defined as the ratio of the number of outcomes to the total number of possible outcomes. The formula is stated as follows:

**Theoretical Probability = Number of favorable outcomes / Total number of possible outcomes**

Now we can certainly identify the difference between the two of them. If you want output based on specific conditions then you will need to apply the theoretical probability formula. On the other hand, if you need to get all the outcomes, you should go with the empirical probability formula.** Empirical probability** arrives at results through solid test-based evidence, while **theoretical probability** is based on established mathematical ideas.

## 4 Examples to Calculate Empirical Probability with Formula in Excel

Now let us see some examples to calculate empirical probability with a formula. Each of them will consider different scenarios for calculation.

### 1. Apply Empirical Probability Formula in Excel While Tossing 1 Coin

Let us assume, we will toss a coin **50** times. There will be 2 possible outcomes- **Head** or **Tail**. Now let’s calculate each of its occurrences with the empirical probability formula.

- First, insert the number
**50**in the**cell range C5:C6**as the**Number of Trials**.

- Then, type
**35**in**cell D5**assuming the**Head**will occur**35**times during those**50**tosses.

- Therefore, type this formula in
**cell D6**to get the**Number of Outcomes**of the**Tail**.

`=C6-D5`

- Following, hit
**Enter**to see the output.

- Now, insert this formula in
**cell E5**to get the**Empirical Probability**of the occurrence of a**Head**.

`=D5/C5`

- Afterward, type this formula in
**cell E6**to get the**Empirical Probability**of the**Tail**.

`=D6/C6`

- Finally, we got the
**Empirical Probability**of**Head**and**Tail**when we toss a coin.

**Read More: ****How to Calculate Probability in Excel (3 Practical Examples)**

### 2. Toss 2 Coins Simultaneously to Get Empirical Probability

In this example, we will consider tossing **2 coins** simultaneously** 100** times. During this trial, we will find the empirical probability of getting** 2 Heads**, **1 Head** and **No Head**. Let’s see the process below.

- First, insert
**100**as the**Number of Trials**in the**cell range C5:C7**.

- Then, type
**35**and**30**as the**Number of Outcomes**for**2 Heads**and**1 Head**respectively in the**cell range D5:D6**.

- Following, type this formula in
**cell D7**.

`=C7-(D5+D6)`

- After this, hit
**Enter**to get the**Number of Outcome**of**No Head**.

- Next, insert the empirical probability formula in
**cell E5**.

`=D5/C5`

- Lastly, apply the
**Autofill**command to get the final outcome.

**Read More: ****Calculating Probability in Excel with Mean and Standard Deviation**

**Similar Readings**

**Calculate Binomial Probability in Excel (with Easy Steps)****How to Calculate Probability of Exceedance in Excel****Make a Probability Tree Diagram in Excel (3 Easy Methods)**

### 3. Calculate Frequency of Empirical Probability Tossing 3 Coins

In this example, we will toss **3 coins** **200** times simultaneously. Then, we will try to calculate the frequency of occurrence of **3 Heads**, **2 Heads**, **1 Head** and **0 Head** with the empirical probability formula. Let’s see how it works.

- In the beginning, type
**200**in the**cell range C5:C8**as the**Number of Trials**.

- Following, insert the
**Number of Outcomes**in the**cell range D5:D8**as shown in the image.

- Now, type this formula in
**cell E5**.

`=D5/C5`

- Then, hit
**Enter**. - Lastly, apply this formula in the
**cell range E6:E8**to get the empirical probability of all the possible outcomes.

**Read More: ****How to Use Normal Probability Distribution in Excel (3 Cases)**

### 4. Experiment of Rolling Dice with Empirical Probability Formula in Excel

In this last example, let us assume a scenario where we will roll a dice** 180 **times. During these trials, there will be possible outcomes of **6 dots**, **5 dots**, **4 dots**, **3 dots**, **2 dots** and** 1 dot **for a total** 6 dot dice**. Now we will apply the empirical probability formula to each of them. Let’s go through the process below.

- First, type
**180**in the**cell range C5:C10**as the**Number of Trials**.

- Then, type the expected
**Number of Outcomes**in the**cell range D5:D10**like this.

- Now, insert this formula in
**cell E5**to get the empirical probability of occurring**6 dots**.

- Lastly, press
**Enter**and then apply the**AutoFill**command to get this final output.

**Read More: How to Calculate Probability Distribution in Excel (with Quick Steps)**

## Things to Remember

- The value of the
**empirical probability**will always lie between**0**and**1**. If the result is**0**, then it determines that the event is an impossible one. Otherwise, it will be a certain event when the output is**1**. - The output of
**empirical probability**is always numeric as it shows the ratio between two values.

## Conclusion

Finally, we are at the end of our article on how to calculate empirical probability with the formula in excel with 4 examples. Let us know your insightful suggestion on this tutorial in the comment box. Follow **ExcelDemy** for more articles like this.