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 –> 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.
To post a comment, please create an account and sign in.
Follow Braingle!