Someone shows you two boxes and he tells you that one of these boxes contains two times as much as the other one, but he does not tell you which one this is. He lets you choose one of these boxes, and opens it. It turns out to be filled with \$10. Now he gives you the opportunity to choose the other box instead of the current one (and skip the \$10 of the first box), because the second box could contain twice as much (i.e. \$20). The Question: Should you choose the second box, or should you stick to your first choice to maximize the expected amount of money? A Hint : If you have \$10, and you could double this with a chance of 1/2, or half it with a chance of 1/2, one would expect an average of 1/2 * \$20 + 1/2 * \$5 = \$12.5 (so you would expect to gain $2.5)!...

general knowledge math & puzzles

  1. Take the first box

  2. Take the second box

  3. Doesn't make difference

  4. Indeterminable

Show answer
Correct Option: A

AI Explanation

To answer this question, we need to consider the probabilities and expected values associated with each choice.

Let's go through each option to understand why it is correct or incorrect:

Option A) Take the first box - This option is correct. If we choose the first box, we are guaranteed to receive \$10. The probability of the other box containing double this amount is uncertain, so it is safer to stick with the known amount of \$10. The expected value of this choice is \$10.

Option B) Take the second box - This option is incorrect. While there is a possibility that the second box contains double the amount of the first box (\$20), there is also a possibility that it contains half the amount (\$5). The expected value of this choice would be the average of these possibilities, which is \$12.5. However, it is important to note that the expected value does not guarantee the actual outcome.

Option C) Doesn't make a difference - This option is incorrect. The choice between the two boxes does make a difference because the first box already guarantees \$10, while the second box has uncertain outcomes.

Option D) Indeterminable - This option is incorrect. The choice can be determined based on the probabilities and expected values associated with each option.

The correct answer is Option A) Take the first box. This option is correct because it guarantees \$10, while the second box has uncertain outcomes.

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