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Boxes of Fruit

You are given three boxes, one contains two apples, one contains two oranges, and the third contains an apple and an orange.

You choose a box at random, and pull a piece of fruit at random from it...to discover it is an apple.

What is the probability that the remaining piece of fruit in this box also is an apple?


Hint: Set up a physical experiment for the situation, using three paper bags for the boxes, three King cards for the apples, and three Queen cards for the oranges. Now, perform the experiment multiple times to gather data.

Try to develop a theroetical model that agrees with the experimental data.


Solution Commentary: This problem is quite old, as I first heard it involving 3 records having either country or jazz on the two sides. The situation was that you were playing records in the dark, picked a record at random, played it to discover some great country songs...if you now flipped the record in the dark, what was the probability that the other side had country as well. Unfortunately, this version no longer works with students, as they ask: What's a record...even worse, some even ask what's country?

Sorry, I am only sharing this story...no solution, as it is better that you argue out your proposed solutions with others. I will tell you that the answer is between 0 and 1!