Empirical Probability: Overview, Questions, Preparation

Empirical Probability is the ratio of the number of times an event has actually happened to the number of experiments that were conducted to get the desired outcome. We can give the formula of Empirical Probability as below:

P(E) = Count the instances when the event has happened/Total count of the experiments or trials performed. 

If M is the number of times when the event has happened and N is the total number of trials that were conducted, this formula can be expressed as below:

P(E) = M/N = Empirical Probability 

How is Empirical Probability different from theoretical probability?

Unlike theoretical probability that just talks about the possibility of an outcome, in this case, numerous trials are conducted and the number of times for which the event has occurred is noted down. Therefore, it is a practical application of probability. 

Pros & Cons of Empirical Probability

While Empirical Probability does have its advantages, it has some limitations as well. Let’s discuss the limitations or cons first:

Cons 

The conclusions drawn from an Empirical Probability might not be always accurate or reliable. This is because it depends on the conditions that were applicable when the event actually occurred. For instance, we all know the probability for 1 appearing when a die is rolled is ⅙. However, during a real experiment, 1 might either appear all the times the die was rolled or may not appear at all. 

The sample size is taken while conducting trials for calculating empirical probability should be large enough to get good enough results. Therefore, if the sample size is less then the chances of finding a precise conclusion get minimised.

Pros 

The primary advantage of Empirical Probability is that it is backed by real experiments or trials. Therefore, it is not influenced by assumptions or predictions. As a result, you can rely on the conclusions drawn based on it, given that the experiments were conducted in a fair way and standard conditions with large sample size. 

You will learn about Empirical Probability in Class X’s Chapter of Probability and its weightage ranges from 2 to 3 marks in the exam. 

1. An experiment was conducted 50 times to find the number of instances for which an event occurred. If the event occurred 5 times, find its Empirical Probability. 

Solution. Empirical Probability = Number of instances for which an event occurred/Number of trials conducted 

Therefore, P(E) = 5/50 = 1/10

2. If P(E) = ⅚ and the number of experiments conducted was 36, find the number of times the event E actually happened. 

Solution. P(E) = Times event E actually happened/Number of experiments conducted 

⅚ = Times event E actually happened/36

Therefore, the number of times event E actually happened is 30.

3. Out of 50 people, 40 choose to drink wine instead of beer. Find the Empirical Probability of someone drinking beer. 

Solution. If 40 people drank wine, 10 people drank beer. Therefore, the Empirical Probability of someone drinking beer can be computed by using its formula:

P(E) = 10/40 = ¼ 

Q: What is Empirical Probability also known as?

Q: What are the three main types of probability?

Q: What is the real-life example of Empirical Probability?

Q: Who invented the theory of probability?

Q: What is the difference between Empirical probability and Classical probability?