Empirical probability is an effective metric to determine the likelihood of an event occurring. It offers the opportunity of relying on past data that helps in making more accurate assumptions about similar occurrences. It’s a really helpful statistical measure in many technical, business and financial applications. Here we’ll look at empirical probability meaning and examples.

## Empirical Probability Meaning

Experimental or empirical probability is the probability that an experiment will have a certain outcome. It’s an experimental process to figure out probabilities based upon the occurrence of an event in the past. The basis of determining empirical probability is using a sample set to find out the number of occurrences of an outcome. The percentage is determined by seeing how many times a given event has occurred out of 100 trials. Professionals use it to determine the beneficial gains and potential risks of business activities such as innovation and investments.

Empirical evidence must be collected to prove or disprove a theory. Empirical probability definition tells us that studies are performed using actual data from the market. Many studies have been conducted to collect empirical data on the capital asset pricing model. As per empirical probability definition, this model should hold in the real world but many studies have disproved it for projecting returns. However, it has its utilities when it comes to estimating an organization’s weighted average cost of capital.

Now that we know the meaning of empirical probability, let’s look at its advantages, some disadvantages and an empirical probability example.

The biggest advantage of empirical probability is that it’s free of assumptions. If we consider a small population where people have to satisfy two conditions for consideration:

• They exercise regularly
• They don’t eat fast food

As per the definition of empirical probability, by counting the number of people, an estimate can be found as to how many people who exercise keep a clean diet, thus determining the probability.

Although it’s a major advantage to have, we can see the two main disadvantages by looking at the empirical probability meaning in detail. They are:

### 1. Risk Of Drawing Incorrect Conclusions

We know that the chances of either outcome in a coin toss are 50%. Now, if an individual tosses it five times and gets heads each time, they may interpret the data falsely. In case a person who’s not fully accustomed to the definition of empirical probability conducts the experiment, they may interpret the result of a coin toss to be heads instead of projecting a 50% probability.

### 2. Small Or Insufficient Sample Size

The accuracy of empirical probability diminishes with smaller sample sizes. Large sample sizes are needed to achieve a good representation of probability. If we consider the case of a coin toss again, using one trial as a sample will reveal a probability of getting heads to be either 100% or zero.

Managers have to recognize effective methods of application and fully understand the meaning of empirical probability to analyze outcomes that can help them strategically.

Professionals can determine which product to launch or how to make it sell more. As we understood from the empirical probability definition, conducting a test to see the preferences of 100 or 1,000 individuals can give a fair idea of what can be expected from a larger base. Empirical probability is determined by calculating the ratio of the number of times an event occurs to the number of times the experiment was performed. It’s represented as P(E)= m/n.

## Empirical Probability Example

Let’s look at some examples of empirical probability:

• ### Empirical Probability Example 1

Out of the 120 people that attended a dinner, 80 preferred mushrooms and others preferred broccoli. To find the empirical probability of a person choosing mushrooms we have to consider 120 as the total number of trials and the 80 people that prefer mushrooms as the number of desired outcomes. Therefore,
P(E)= 80/120
Hence, the probability of a person choosing mushroom is 66.67%

• ### Empirical Probability Example 2

A boy was asked to draw one marble out of a bag of four marbles, where each is colored red, blue, yellow or green. This was repeated 40 times. Red was drawn 15 times, yellow 12 times, green 6 times and blue 7 times. The probability of drawing a blue marble at random is 7/40, which is 17.5%

Empirical probability can be similarly applied to different scenarios, including in business, to estimate the probability of making gains or losses.

Using empirical probability in business helps tackle hurdles by analyzing them and finding a way past them or eliminating them entirely. Harappa’s Creating Solutions program is an online problem-solving course that’ll teach you to be creative when coming up with solutions. Learn tools like the AQR framework to evaluate data and understand the type of research needed before analysis. Use the synthesis technique to synthesize the results of the analysis and draw actionable insights. Ask successive ‘WHYs’ to get to the root cause of a problem as our faculty equips you with every tool to break down complex problems and manage them effectively.

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