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## Cash Giveaway

Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

 Fun: (2.32) Difficulty: (1.81) Category: Probability Submitted By: tommo

I take three envelopes and put \$5 in the first, \$10 in the second and \$20 in the third. The average value in the envelopes is \$11.66. I mix up the envelopes and pick two at random. I give you a choice of the two envelopes; you pick one and look inside to see \$10. I then give you the option of swapping to one of the other envelopes. How much would you get on average by swapping your choice of envelopes?

On average you would win \$12.50 instead of \$10 because the expectation, E(x)=0.5x\$5+0.5x\$20=\$12.50.
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 Posted by Lilman_220 on Apr 17, 2002 Say What?! Posted by ~superhack~ on Jun 11, 2002 Not bad. This one made me think for once. Posted by on Jul 29, 2002 The average changes to \$12.50 when you take \$10 out of the equation. Posted by javaguru on Dec 23, 2008 I said \$2.50. Since you already have \$10, on average you gain \$2.50 by switching. Posted by Abhi8 on Aug 23, 2010 If we swap there is a 50/50 chance of getting 5 or 20. Suppose we play this game 100 times we should get 5 –> 50 times & 20 –> 50 times (on average). Which means we would stand to lose 250 and gain 500. Which is an average gain of 2.5 overall.