# What is the difference between empirical and theoretical probability?

May 2, 2018

See explanation below

#### Explanation:

Imagine the experiment of flipping a coin and counting the number of faces and crosses.

Theoretically $P \left(f\right) = \frac{1}{2} = 0.5$ by Laplace law (Probability is the quotient between favourable cases and possible cases)

But your experiment (20 times repeated) shows the following results

$f , f , f , c , c , c , f , c , f , f , f , c , c , f , c , f , c , f , c , f$

$P \left(f\right) = \frac{11}{20} = 0.55$

Obviously $P \left(c\right) = \frac{9}{20} = 0.45$

In this experiment the empirical probability (based on experience) is slightly different from theoretical

If you repeat other 20 times you will calculate the probability that will be equal or not to above results. The theory of probability says that if you increase the number of coin toss, the probability aproaches to the theoretical value (if coin is well balanced)

Hope this helps