There are three cards in a box. Both sides of one card are black, both sides of one 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 the same colour as the one side we observed?
Show Hint
- \( \frac{3}{4} \)
- \( \frac{2}{3} \)
- \( \frac{1}{2} \)
- \( \frac{1}{3} \)
The Correct Option is C
Solution and Explanation
When we observe one side, we are equally likely to have observed the black side or the red side.
The probability that the opposite side is the same as the observed side depends on the card chosen.
For the black card (with both sides black), the opposite side is certainly black, and for the red card (with both sides red), the opposite side is certainly red.
For the mixed card (one red and one black side), the probability of the opposite side matching is \( \frac{1}{2} \).
Therefore, the overall probability is \( \frac{1}{2} \).
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