A \"risk-neutral\" person is one who will pay exactly the expected value for any

Question

A "risk-neutral" person is one who will pay exactly the expected value for any bet. Thus, a risk-neutral person would pay you $1 (nothing more and nothing less) for a bet where you pay $2 if heads comes up on a fair coin and nothing if tails comes up. Assume that Ted is risk-neutral. Ted is offered the following proposition/bet. I am going to flip a fair coin until a tails comes up. Let N be the number of times that heads comes up (before the first tail). I will pay Ted 2^N dollars. For example, if tails comes up first, Ted will get one dollar, but if four heads come up before the first tails then Ted gets 24 or S16. How much will Ted pay for the bet?

Explanation / Answer

expected Sum of game =probability of 0 head and 1 dollar+1 heads and 2 dollar+2 heads and 4 dollars+.......

=(1/2)*1+(1/4)*2+(1/8)*4+(1/16)*8+............=(1/2)+(1/2)+(1/2)+(1/2)+.............

which leads to infinite sum.

therefore any amount of money will fall short to pay for the game.

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