A ball is drawn from a bag with \(3\) red and \(1\) blue ball, then a fair coin is flipped. Compute the four color-coin path probabilities and evaluate equal-outcome fairness.

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Assign red and blue probability 1/2 before each coin result, giving four paths of 1/4; call the process fair because there are two color names.

Red-head and red-tail each have probability 3/8, while blue-head and blue-tail each have probability 1/8, so the four outcomes are not equally likely.

Assign all four color-coin outcomes probability 1/4 because the coin is fair; they total 1, so call the process fair.

Use probabilities 3/8, 3/8, 1/8, and 1/8; because they total 1, incorrectly call the unequal outcomes fair.

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Curriculum context

Course: Math III
Standard: S-MD.6
Category: Statistics and Probability
Domain: Using Probability to Make Decisions
Objective: Use probabilities to make fair decisions in more complex settings.
Problem type: List ordered path probabilities and test equal-outcome fairness