### Brain Teasers

# Cash Giveaway

Probability
Probability 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?

### Answer

On average you would win $12.50 instead of $10 because the expectation, E(x)=0.5x$5+0.5x$20=$12.50.Hide Answer Show Answer

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