There are two ways to calculate probability:
- using math to predict
- by actually observing the event and keeping score.
Theoretical probability uses math to predict the outcomes. Just divide the favorable outcomes by the possible outcomes.
Experimental probability is based on observing a trial or experiment, counting the favorable outcomes, and dividing it by the total number of times the trial was performed.
Let's look at this example: we tossed a coin 36 times and recorded the outcomes:
H, T, H, H, T, T, H, T, T, T, T, T,
T, T, T, H, H, T, H, H, T, H, H, H,
H, T, H, H, T, H, H, T, H, H, T, H
Based on this experiment:
- Experimental probability of flipping Heads is
or about 
and Tails is 
or about 
- Theoretical probability of flipping Heads is
and Tails is
Example 1
A die was rolled 50 times. These are the results:
6 5 4 5 4 1 3 4 2 6 2 6 1 6 6 4 2 4 5 5 1 1 1 5 3 a) What is the experimental probability of rolling each number? b) And how do these compare to the theoretical probabilities? |
.
or 
or 
or 
, which is 9 percentage points less than its theoretical probability.