# Theoretical vs. Experimental Probability

In this video, we are going to learn about the differences between theoretical probability and experimental probability.

Let’s use rolling a dice as an example. Use P to represent probability.

Theoretical: The ratio of possible ways that an event can happen to the total number of outcomes.
$P(even)\frac{3}{6}=\frac{1}{2}$
Theoretically, the probability of rolling a even number on a dice ranging from 1 to 6 would be $\frac{3}{6}$, or simply just $\frac{1}{2}$.

$P(1)\frac{1}{6}$
To roll a one, the theoretical probability would be $\frac{1}{6}$.

On a larger scale, it also means that theoretically, the probability
of rolling one number is the same.

Experimental: The ratio of the number of times an event happens to the total number of outcomes.

Let’s use the following table to find the experimental probability after rolling a dice 60 times.

 Outcome Frequency 1 15 2 18 3 7 4 20 5 2 6 8

$P(even)\frac{8+20+8}{60}$
Experimentally, the probability of rolling a even number would be the sum of the frequency for even outcomes to the total number of trials.
$P(even)\frac{36}{60}$, or simply just $\frac{3}{5}$

$P(1)\frac{15}{60}$
To roll a one, the experimental probability would be $\frac{1}{4}$.

Note that the probability of rolling each number is different, as well as when compared to the theoretical probabilities.