Question

Three boxes contain gold, silver, and bronze coins. One box has only gold, one only silver, one only bronze. Labels are incorrect. You choose one box and draw one coin at random. It’s gold, what is the probability you chose the box labeled "Silver"?

• A. 1/3
• B. 1/2
• C. 2/3
• D. 0
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Hint:

In mislabeled box puzzles, use the drawn item to identify the true box, then check its label against incorrect labeling to determine probabilities.

Answer 1

The Correct Option is D

- Step 1: Recall setup. Three boxes: gold, silver, bronze. Labels incorrect. Drew a gold coin from a chosen box.
- Step 2: Identify the box chosen. From Question 15, drawing a gold coin means you chose the gold box, as only the gold box has gold coins.
- Step 3: Check the label. Since labels are incorrect, the gold box is not labeled "Gold." It could be labeled "Silver" or "Bronze."
- Step 4: Analyze probability. You chose the gold box (confirmed by drawing gold). However, the question asks for the probability of choosing the box labeled "Silver." Since labels are incorrect, the box labeled "Silver" is either the gold box or bronze box, but only the gold box yields gold.
- Step 5: Clarify condition. Drawing a gold coin fixes the choice to the gold box. If the gold box is labeled "Silver," the probability is 1, but typically, this puzzle assumes random box choice initially. Recompute: Initial choice probability is 1/3, but the condition (gold coin) eliminates other boxes. The box labeled "Silver" cannot be the silver box (no gold coins), so it’s impossible to draw gold from the box labeled "Silver."
- Step 6: Final conclusion. Probability of choosing the box labeled "Silver" and drawing gold is 0, as it cannot yield gold. Option (4) 0 is correct.
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