# What is the difference between empirical and theoretical probability?How well we understand the difference between empirical and theoretical probability is important part of our ability to apply...

What is the difference between empirical and theoretical probability?

How well we understand the difference between empirical and theoretical probability is important part of our ability to apply probability to a real world set of data. Please give two or three examples of professions where probability could be used and please explain your answer.

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### 1 Answer

The term "empirical" involves the presence of an experiment, therefore the empirical probability is presented as a percentage that results from an experiment.

The theoretical probability will give answers based on formulas, without the need of conducting any experiment.

Choosing one of these probabilities depends on the needs.

For instance, to calculate the theoretical probability, we'll use the formula:

P = the number of ways an eveniment can happen/the total number of possibilities

If we want to determine the theoretical probability of picking a lemon candy, from a jar where we have 6 lemon candies and 4 mint candies, we'll use the formula:

P = 6/(6+4)

P = 6/10

P = 3/5

The theoretical probability of picking a lemon candy is 3/5.

If you want to determine the empirical probability, you'll have to repeat the operation of picking a candy and to determine how often the lemon candy has been picked. The more you'll reapeat the picking action, the more accurate will be the result.