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 the other coins in that box are also gold?

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

For probability puzzles with mislabeled boxes, focus on the outcome (e.g., drawing gold) to identify the only possible box, simplifying the probability calculation.

Answer 1

The Correct Option is D

- Step 1: Understand the setup. Three boxes: one gold, one silver, one bronze. Labels are incorrect (e.g., gold box is not labeled gold). Draw one coin from a chosen box, and it’s gold.
- Step 2: Analyze outcomes. Choose a box randomly (1/3 chance each). Draw a coin. Since it’s gold, the box must have at least one gold coin.
- Step 3: Identify the box. Only the gold box contains only gold coins. If you chose the gold box and drew a gold coin, all other coins in that box are gold (probability 1).
- Step 4: Consider other boxes. Silver box has only silver coins, bronze box has only bronze coins. Drawing a gold coin rules out these boxes, as they cannot yield gold.
- Step 5: Confirm probability. Since the coin is gold, you must have chosen the gold box. Thus, all other coins in that box are gold, so probability is 1.
- Step 6: Verify with options. Probability of 1 matches option (4).
- Step 7: Final conclusion. Option (4) 1 is the correct answer.
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