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Chapter 12: Problem 2

Describe the difference between theoretical probability and experimental probability.

Short Answer

Expert verified
Theoretical Probability relies on mathematical reasoning and models for calculation, using the number of ways an event can occur and the total number of equally probable outcomes. Experimental Probability, on the other hand, is calculated based on conducting experiments, using the number of times event occurs and the total number of trials conducted. The key difference lies in their method of calculation - one being theory-based, and the other being experiment-based.

Step by step solution

01

Understanding Probability

The concept of probability in mathematics gives us an idea, based on certain calculations or observations, about how likely or unlikely an event is to occur.
02

Define Theoretical Probability

Theoretical Probability is a probability that is calculated using mathematical models or reasoning. For a given event E, it's defined as the ratio of the number of ways E can occur, to the total number of equally likely outcomes in the sample space. It is given by the formula: \( P(E) = \frac{Number \, of\, favorable \, outcomes}{Number\, of\, total\, possible\, outcomes} \)
03

Define Experimental Probability

Experimental Probability, also known as Empirical Probability, is a probability calculated by conducting an experiment, or a series of experiments, and observing the outcomes. Given an event E, experimental probability of E happening, denoted as \( P(E') \), is the ratio of the number of times E occurs, to the total number of trials conducted. The formula would be: \( P(E') = \frac{Number \, of\, times \, E\, occurred}{Total\, number\, of\, trials} \)
04

Highlight the Differences

The main difference between theoretical and experimental probability lies in their calculation method. Theoretical probability is calculated based purely on mathematical reasoning and models, relying on the equally likely outcomes in the sample space. On the other hand, experimental probability is calculated based on the outcomes observed from conducting experiments or trials.

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