Let's remember how to find the theoretical probability of a specified event of a probability experiment.
lTheoretical Probability = Number of favorable outcomes/Total number of outcomes
We can see that this probability depends on the number of possible outcomes. Therefore, the theoretical probability depends on the size of sample space of the experiment.
Experimental Probability
Now, let's recall how to find the experimental probability of a specified event of a probability experiment.
lExperimental Probability = Number of successes/Total number of trials
We can see that this probability depends on the number of trials that took place.
Conclusion
The main difference between these probabilities is that the theoretical probability comes from the knowledge of every possible outcome of an experiment, while the experimental probability comes from the results of a number of trials. Let's illustrate this difference with an example.
Example
Consider that we flip a coin.
We know that there are 2 possible outcomes, either we flip heads or we flip tails. We can write a table with the theoretical probability of each of these outcomes.
Outcome
Theoretical Probability
Heads
1/2
Tails
1/2
Now we will flip a coin 10 times. Let's make a table with the number of successes of each outcome and find the experimental probability.
Outcome
Number of Successes
Experimental Probability
Heads
3
3/10
Tails
7
7/10
We can see that the experimental probability differs from the theoretical probability. Let's flip a coin 50 times now!
Outcome
Number of Successes
Experimental Probability
Heads
26
26/50 = 13/25
Tails
24
24/50 = 12/25
We can see that, if we increase the number of trials, the difference between the experimental probability and the theoretical probability is reduced. In general, the experimental probability approaches the theoretical probability as we increase the number of trials in an experiment.
