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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.
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}.

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

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}

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.