When we look at experimental and theoretical probability, it helps to know how both ideas work in predicting outcomes.

Theoretical Probability is what we think will happen based on math. For example, if you flip a fair coin, the theoretical probability of it landing on heads is $P(\text{heads}) = \frac{1}{2}$. This means that if you flip the coin many times, you would expect about half of the flips to be heads and half to be tails.

Experimental Probability, however, comes from real-life experiments or tests. If you flip a coin 100 times and get heads 60 times, your experimental probability of heads would be $P(\text{heads}) = \frac{60}{100} = 0.6$. This number can be different from the theoretical probability, especially if you don’t have many trials.

So, can experimental probability sometimes be more important than theoretical probability when predicting outcomes? Yes, it can. This is especially true when the theoretical model doesn’t show all the real-world details. For example, if you are rolling a die that is not completely fair, the theoretical probability for each side is $\frac{1}{6}$. But if you do many rolls and notice that a six comes up more often, like $P(6) = 0.4$, then you have found something different.

In these cases, using experimental probability might give you a better idea of what to expect in future rolls. This means that while theoretical probability gives us a starting point, experimental probability can show us how things really turn out and might be more trustworthy for some predictions. It’s important to use both when making guesses about the future!