diff --git a/source/fun/boxes.ptx b/source/fun/boxes.ptx new file mode 100644 index 0000000..bbcf0ff --- /dev/null +++ b/source/fun/boxes.ptx @@ -0,0 +1,74 @@ + + + + + Boxes + + + +

+ The following is not for credit and will not be covered on any quiz or exam. + This is just for fun. +

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+ A superintelligent robot named Bob waits in a room with two boxes. + Box 1 contains $1000. + Box 2 is a mystery box containing a secret amount of money. + Bob will offer you the choice: +

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    + You can take the mystery box alone, or +

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    + You can take both boxes. +

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+ Bob is very accurate at predicting ahead of time what people will do. + If Bob thinks that you'll choose to take only the mystery box, he'll put $1 million dollars in the mystery box. + If Bob thinks that you'll choose to take both boxes, he'll put nothing in the mystery box. + Bob made his prediction and placed $1 million or $0 in the mystery box before you entered the rooms and learned the rules of the game. +

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+ Would you take just the mystery box? Or would you take both boxes? +

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+ Let \alpha be the probability that Bob accurately predicts your choice. + Write an expected value formula for the strategy of choosing just the mystery box in terms of \alpha. + Write an expected value formula for the strategy of choosing both boxes in terms of \alpha. + Which strategy has a higher expected value? +

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+ Let \beta be the probability that Bob predicts that you'll take both boxes. + Write an expected value formula for the strategy of choosing just the mystery box in terms of \beta. + Write an expected value formula for the strategy of choosing both boxes in terms of \beta. + Which strategy has a higher expected value? +

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\ No newline at end of file diff --git a/source/main.ptx b/source/main.ptx index 85332b5..d2c8e33 100644 --- a/source/main.ptx +++ b/source/main.ptx @@ -62,7 +62,14 @@ Exam Review + + + + Just for Fun + + +