4. mp be precise compare and contrast relative frequency and theoretical probability.

Answer:

Relative frequency is the ratio of the number of times an event occurs to the total number of trials in an experiment. Theoretical probability is the ratio of the number of favorable outcomes to the total number of possible outcomes based on mathematical reasoning. The main differences are: 1. Source - Relative frequency comes from actual experiments or observations, while theoretical probability is based on assumptions and mathematical models. 2. Value - Relative frequency may vary from experiment to experiment, but as the number of trials increases, it tends to approach the theoretical probability. For example, when flipping a fair coin, the theoretical probability of getting heads is 0.5. If we flip the coin 10 times, the relative frequency of getting heads might be different from 0.5, but if we flip it 1000 times, it will likely be close to 0.5.

Explanation:

Step1: Define relative frequency

It is based on experiment results.

Step2: Define theoretical probability

It is based on math - based assumptions.

Step3: Compare sources

Experiment vs math model.

Step4: Compare values

Variable in short - run, converges in long - run.