Multiple choice

There are three cards in a box. Both sides of one card are black, both sides of second card are red, and the third card has one black side and one red side. We pick a card at random and observe only one side. What is the probability that the opposite side is of the same colour as that of the one side we observed?

  1. 3/4

  2. 2/3

  3. 1/2

  4. 1/3
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B Correct answer
Explanation

There are 6 sides total: 2 black (card 1), 2 red (card 2), 1 black and 1 red (card 3). If you observe a black side, it could be one of the 2 sides of card 1 or the 1 black side of card 3 (3 possibilities). In 2 of those cases, the other side is black. Probability = 2/3.

AI explanation

This problem is solved using the principle of restricted choice, considering each visible colored face as a distinct possibility. There are 3 cards with 2 faces each, resulting in 6 equally likely faces that could be observed. If you observe a black face, it could be either face of the all-black card or the single black face of the mixed card; only 2 of these 3 possibilities have a black face on the opposite side. The same logic applies if a red face is observed. Therefore, the overall probability that the opposite side is the same color is 2/3.

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