What causes experimental probability to match theoretical probability?

Actually doing the experiment?

To increase the amount of trials

Experimental probability is the result of performing an actual experiment or analysis on a specific event or outcome over a certain number of trials. The theoretical probability, on the other hand, is the probability calculated based on mathematical principles and assumptions without conducting any actual experiments.

There are various factors that can cause experimental probability to match theoretical probability, indicating a good agreement between the observed results and the predicted probabilities. Here are a few reasons for this:

1. Large sample size: As the number of trials or observations increases, the experimental probability tends to converge towards the theoretical probability. This is known as the Law of Large Numbers. When the sample size is sufficiently large, the influence of random variations decreases, leading to experimental results that align closely with the theoretical probabilities.

2. Independent events: For probabilities to match, the events being analyzed should be independent of each other. Independence means that the outcome of one event does not affect the outcome of another. When events are independent, the experimental results tend to approach the theoretical probabilities more accurately.

3. Balanced and fair conditions: To ensure accurate results, it is important that the experiment is conducted under balanced and fair conditions. This means that each possible outcome has an equal chance of occurring. If the experiment is biased or unfair, the experimental probability may not match the theoretical probability.

4. Consistency with known principles: When the theoretical probability is calculated based on well-established mathematical principles or models, and the experimental probability matches the theoretical result, it indicates that the underlying assumptions and principles are reliable and applicable to the situation.

To summarize, experimental probability can match theoretical probability when there is a large sample size, events are independent, conditions are fair, and the theoretical calculation is consistent with known principles.