Question

click to review the online content. then answer the question(s) below, using complete sentences. scroll down to view additional questions. online content: site 1 how are theoretical probability and experimental probability related?

Explanation:

Theoretical probability is calculated using mathematical reasoning about the likelihood of an event, based on the total number of possible outcomes and the number of favorable outcomes (formula: \( P(\text{event})=\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \)). Experimental probability is found by conducting trials (experiments) and dividing the number of times the event occurs by the total number of trials (formula: \( P(\text{event})=\frac{\text{Number of times event occurs}}{\text{Total number of trials}} \)). As the number of trials in an experiment increases, experimental probability tends to approach theoretical probability (this is related to the Law of Large Numbers). So they are related in that experimental probability can approximate theoretical probability with more trials, and both describe the likelihood of an event, with theoretical being based on reasoning and experimental on actual trials.

Answer:

Theoretical probability is calculated using mathematical reasoning (e.g., \( P(\text{event})=\frac{\text{favorable outcomes}}{\text{total outcomes}} \)) to determine the likelihood of an event, while experimental probability is found by conducting trials (e.g., \( P(\text{event})=\frac{\text{event occurrences}}{\text{total trials}} \)). As the number of experimental trials increases, experimental probability tends to approach theoretical probability (due to the Law of Large Numbers), and both describe the likelihood of an event—one through reasoning, the other through actual experimentation.