Use the given table, which lists six possible assignments of...

Use the given table, which lists six possible assignments of probabilities for tossing a coin twice, to answer the following questions.
Which of the assignments of probabilities should be used if the coin is known to be fair?

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Key Concepts

Fair Coin

A fair coin is one in which the probabilities of landing heads or tails are equal. This concept is crucial when modeling coin toss experiments, as it implies that the coin has no bias towards either outcome.

Uniform Probability Distribution

A uniform probability distribution assigns the same probability to every event in the sample space. In the context of a fair coin, each outcome—whether it is a single toss or a sequence of tosses—should be equally likely, reflecting the absence of bias.

Sample Space

The sample space is the complete set of all possible outcomes of an experiment. For a coin tossed twice, the sample space includes all possible sequential outcomes, and if the coin is fair, each outcome in the sample space is assigned an equal probability.

Independence

Independence means that the outcome of one coin toss does not affect the outcome of another. This property is essential when analyzing multiple tosses because it supports the assumption that each toss is governed by the same fair probability distribution.

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