Multiple choice

Box I contains 2 gold and 3 silver coins, Box II contains 3 gold and 2 silver coins, and Box III contains 1 gold and 4 silver coins. A box is chosen at random and a coin drawn from it is found to be gold. What is the probability that it came from Box II?

  1. 3/8

  2. 1/2

  3. 9/14

  4. 5/14
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C Correct answer
AI explanation

Using Bayes theorem, the probability that the chosen box is Box II given that a gold coin is drawn equals the probability of drawing gold from Box II divided by the total probability of drawing gold from all three boxes. The probability of choosing Box II and drawing gold is (1/3) * (3/5) = 1/5, and the total probability of drawing gold is (1/3)(2/5) + (1/3)(3/5) + (1/3)*(1/5) = 6/15. The result is (1/5) divided by (6/15), which equals 9/14.

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