Suppose for a Valentine's Day gift you are asked to choose only one of three identical looking boxes of chocolates, but you are told that inside one of the boxes are chocolates AND a diamond ring! You pick a box, say the first on the left, and your Valentine, who knows what's inside the boxes, opens another box, say the middle one, which has only chocolates. He then says to you, "Do you want to pick the box on the right?" Is it to your advantage to switch your choice? Please explain.
(Due February 15, 2008)
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2 comments:
It's been quiet all week. Let's see if I can help begin a discussion.
Can anyone think of a reason why it might not make a difference to switch or not to switch?
This is Mr. Tomlin's answer to Problem 9: Choosing the box on the left leaves me with a one-in-three chance of having thre box of chocolates with the diamond ring. If my Valentine chooses the box in the center knowing that it only contains chocolates, that improves my chances to one in two. Switching my box from the box on the left to the one on the right will not improve my chances, but the fact that I was given the option might indicate that I may not be in possession of the correct one.
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