Why is theoretical probability important?
It’s useful in that we can compare it with experimental probability.
Theoretical probability gives us something to look towards and “expect.” As the number of trials (say a trial = flipping a coin) increases, the experimental probability gets closer and closer to the theoretical probability.
Keeping in line with the idea of flipping a coin, theoretical probability can be thought of as the number of ways that an event, E, can occur over all possible outcomes. So, the theoretical probability of getting heads when you flip a fair, balanced coin is 1 (only one way to get heads) over 2 (two possible outcomes – heads and tails.) Were we to conduct trials/experiments and keep flipping a coin, we would see the probability of getting heads, which we can call P(H), getting closer and closer to 0.5/50%.
Experimental probability is commonly used in research and the sciences, but in order for it to be accurate/meaningful the sample size must be very large. I think of theoretical probability as a benchmark, something to judge and compare your experimental/empirical probability with.