In basic probability, which statement best describes the difference between experimental probability and theoretical probability?

• A. Experimental probability is always exact, while theoretical probability is always an estimate based on limited data.
• B. Experimental probability is based on observed results from repeated trials, while theoretical probability is calculated from a model of equally likely outcomes.
• C. Experimental probability applies only to independent events, while theoretical probability applies only to dependent events.
• D. Experimental probability is computed using permutations and combinations, while theoretical probability is found only by running simulations.

Answer: (B)

Verified step by step guidance

1. Step 1: Understand the definition of theoretical probability. Theoretical probability is calculated based on a mathematical model assuming all outcomes are equally likely. It is given by the formula: \(P(\text{event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}\).
2. Step 2: Understand the definition of experimental probability. Experimental probability is determined by conducting actual experiments or trials and observing the outcomes. It is calculated as: \(P(\text{event}) = \frac{\text{Number of times event occurs}}{\text{Total number of trials}}\).
3. Step 3: Recognize that theoretical probability is derived from known or assumed models without performing experiments, while experimental probability relies on real data collected from repeated trials or observations.
4. Step 4: Note that experimental probability can vary from theoretical probability due to randomness and sample size, but as the number of trials increases, experimental probability tends to approach theoretical probability (Law of Large Numbers).
5. Step 5: Use this understanding to evaluate the given statements and identify that the correct distinction is that experimental probability is based on observed results from repeated trials, whereas theoretical probability is calculated from a model assuming equally likely outcomes.