### Brain Teasers

# Cash Giveaway

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

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

## What Next?

View a Similar Brain Teaser...

If you become a registered user you can vote on this brain teaser, keep track of which ones you have seen, and even make your own.

### Solve a Puzzle

## Comments

Say What?!

Not bad. This one made me think for once.

Jul 29, 2002

The average changes to $12.50 when you take $10 out of the equation.

I said $2.50. Since you already have $10, on average you gain $2.50 by switching.

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 â€“> 50 times & 20 â€“> 50 times (on average). Which means we would stand to lose 250 and gain 500. Which is an average gain of 2.5 overall.

To post a comment, please create an account and sign in.

## Follow Braingle!