Cash GiveawayProbability puzzles require you to weigh all the possibilities and pick the most likely outcome.
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?
AnswerOn 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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