Math Is Fun Forum

freddogtgj

Member

Registered: 2006-12-02

Posts: 54

Probablilty Help

Hi people can anyone help me in this question:

Gonzo plays a series of independent games. At the start of each game he pays £1 then rolls a fair 6-sided die. If he obtains a 6 he receives £C; otherwise he receives nothing.  The game continue until he throws a 1, when the series of games stop.  Find the expected amount he wins and hence state the value of C for which the game is fair (the expected amount he wins is zero).

I'm thinking it has something to do with the Gamblers Ruin problem if you're familiar with it.

Thanks in advance

Last edited by freddogtgj (2007-10-15 10:07:48)

freddogtgj

Member

Registered: 2006-12-02

Posts: 54

Re: Probablilty Help

Don't worry people I have it solved.

If you're wondering how, it's to do with the Expectation of Total Probability and not the Gambler's Ruin Problem I originally stated.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Probablilty Help

Very true. Basically, he expects to win (-1)x5/6 + Cx1/6 per game, and so you equate that to 0 and produce a fair game-value of C=£5.

The gambler's ruin problem is considerably more interesting. It says that if you play a fair game against a casino with infinite money, then you will eventually lose everything regardless of what you started with. It's associated with random walks, which I have recently become interested in.

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Why did the vector cross the road?
It wanted to be normal.