ANSWER
Theoretical probability: based on mathematics. Does not depend on the number of repetitions of the experiment.
Experimental probability: depends on the repetitions of the experiment and the favorable outcomes observed.
As the number of repetitions of the experiment increases, the experimental probability gets closer to the theoretical probability.
EXPLANATION
Theoretical probability gives information about what outcome is expected based on mathematics. For example, let's say that the experiment is rolling a die and we want to know the probability of rolling a 3. Mathematically, if we assume the die is fair, the theoretical probability of rolling a 3 is,
[tex]P(3)=\frac{1}{6}\approx0.167[/tex]Because out of the 6 faces of the die, only one has the number 3.
Experimental probability is the one obtained by repeating the experiment and observing the outcomes. Let's go back to the die example above. To find the experimental probability of rolling a 3, we will have to roll the die many times and count how many of those rolls were a 3. Let's say we roll the die 60 times and we obtain the following results:
• 1: 8 times
,• 2: 11 times
,• 3: 12 times
,• 4: 10 times
,• 5: 9 times
,• 6: 10 times
The experimental probability of rolling a 3 is,
[tex]P(3)=\frac{12}{60}=\frac{1}{5}=0.2[/tex]Note that the experimental probability obtained in this experiment is greater than the theoretical probability. This can happen and also the other way around, that the experimental probability is less than the theoretical probability.
Also, by the law of large numbers, it is expected that, as the number of repetitions of the experiment increases, the experimental probability will get closer and closer to the theoretical probability. In other words, if we repeat the experiment of rolling the die 100 times, then 500 times, and so on, the experimental probabilities obtained will be closer and closer to the theoretical probability found before.
