Box 1 has 3 gold and 1 silver coin, box 2 has 1 gold and 3 silver, and box 3 has 2 gold and 2 silver. A box is picked at random and a coin drawn from it. What is the probability that the coin is gold?

\frac{1}{4}

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\frac{1}{3}

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\frac{1}{2}

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\frac{3}{4}

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CorrectNot quiteAnswer C

Correct answer: C

Each box has probability $\frac{1}{3}$ : $\frac{1}{3}\left(\frac{3}{4} + \frac{1}{4} + \frac{2}{4}\right)$ .
$\frac{1}{3} \times \frac{6}{4} = \frac{1}{2}$ .

Worth noting

$\frac{1}{3}$ is the chance of picking any one box, not of drawing gold.

Ten questions from Conditional Probability & Bayes' Theorem, at your own pace.

Explanation