FILE No.140Unsolved
There are three cards: red on both sides, white on both sides, and red on one side and white on the other. You draw one with your eyes closed and place it on the table, in a random orientation. The top face is red.
What is the probability that the back of that card is also red?
If you get stuck, open the hints one at a time, in order.
How many red "faces" are there in all?
Count the two red faces of the same card separately.
What are the 3 ways for the top to be red?
What is the probability that the back of that card is also red?
Choose the answer closest to the truth.
2/3
The answer is "2/3."
There are 3 red faces in all (two from the double-red card, one from the red/white card). Of the 3 ways the top can be red, the back is also red in the 2 ways that belong to the double-red card.
1/2 comes from thinking "it's one of the remaining two cards," which overlooks how the red faces are counted.
Because you think "one of the remaining two cards" and say 1/2.
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