You are on the show "Who Wants to be a Millionaire." You just won $64,000 and you now have the opportunity to go for $125,000. You realize that you don't know the question at all and would have to just guess. You have a 25% chance of getting it right. So you have two options ... 1) walk out and go home with $64,000 or 2) guess on the question ... if you get it right you would get $125,000 if you got it wrong you'd only take home $32,000.

Explain what you would do using mathematics and using expected value.

Question

You are on the show "Who Wants to be a Millionaire."  You just won $64,000 and you now have the opportunity to go for $125,000.  You realize that you don't know the question at all and would have to just guess.  You have a 25% chance of getting it right.  So you have two options ... 1) walk out and go home with $64,000 or 2) guess on the question ... if you get it right you would get $125,000 if you got it wrong you'd only take home $32,000.

Explain what you would do using mathematics and using expected value.