You roll a six-sided die 60 times. The table shows the...

You roll a six-sided die 60 times. The table shows the results. For which number is the experimental probability of rolling the number the same as the theoretical probability? (See Example 5.)

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Key Concepts

Experimental Probability

Experimental probability is calculated by taking the number of times an event actually occurs and dividing it by the total number of trials in the experiment. It relies on observed outcomes and can be affected by sample size and random chance, often differing from the theoretical probability, especially when the number of trials is small.

Theoretical Probability

Theoretical probability is the likelihood of an event occurring based on a model or set of assumptions about the system, without performing any experiments. It is determined using mathematical calculations under the assumption that all outcomes are equally likely, providing an idealized value for comparison with experimental results.

Uniform Probability Distribution

A uniform probability distribution is one in which every outcome in the sample space has an equal chance of occurring. In the context of rolling a fair die, this assumption means that each face has an equal theoretical probability, which serves as the baseline for comparing with experimentally obtained probabilities.

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