What does the experimental probability approach as trials increase?

The concept of experimental probability is based on the idea that as the number of trials increases, the experimental probability of an event will converge towards the theoretical probability of that event. This convergence occurs because repeated trials provide a larger sample size, which leads to results that better reflect the true underlying probabilities based on all possible outcomes.

In the context of probability, theoretical probability is calculated based on the possible outcomes in a perfect scenario. For example, if you roll a fair six-sided die, the theoretical probability of rolling a 3 is 1 out of 6, or approximately 16.67%. As you conduct more trials, such as rolling the die many times, you may initially find varying experimental probabilities based on your results. However, with a sufficient number of rolls, the experimental probability of rolling a 3 will start to approximate this theoretical probability more closely.

This principle is grounded in the law of large numbers, which states that as the number of trials increases, the average of the results obtained from those trials will get closer to the expected value – in this case, the theoretical probability. Hence, the correct answer is that experimental probability approaches an approximation of theoretical probability as trials increase.