Probability Puzzle

TredWel · 12-14-2003, 12:33 AM

Actually created this one, to prove a point to a friend. The problem is, I'm getting two different answers. I'm fairly confident about which one is the correct answer, but can't find the flaw in my logic for the other answer.

With that prelude, I offer the question to you.

We're going to play a game. I've got a weighted coin, such that Heads comes up 60% of the time, and naturally Tails occurs 40% of the time. The game works as follows: I flip the coin. If the coin lands Heads, I pay you $1, and I flip the coin again. If the coin lands Tails, you pay me $1, and we stop playing.

How much do you expect to win or lose by playing this game?

Katon · 12-14-2003, 08:35 AM

A little under 40 cents, I'd say. QuikSand, I think you missed that as soon as TredWel wins one the game stops.

QuikSand · 12-14-2003, 08:38 AM

Quote:

Originally posted by Katon
QuikSand, I think you missed that as soon as TredWel wins one the game stops.

Thanks, I did miss that. (Was wondering what's so tough...)

QuikSand · 12-14-2003, 08:46 AM

How about 50 cents.

rdo · 12-14-2003, 09:32 AM

I get the same answer as Quiksand. You expect to lose $0.50.

From (1-2x)/(1-x) where x is the probablity of a head.

TredWel · 12-14-2003, 01:33 PM

Yes, you can expect to win 50 cents by playing this game.

I double checked my summation with Maple, and found my error.

Wolfpack · 12-15-2003, 11:40 AM

So, this is one of those quirky things where expectation could never meet real life, simply because you are playing with whole numbers (winner always gets $1) and the expectation is a fraction (.50).

finkenst · 12-15-2003, 11:59 AM

Maple Leafs · 12-15-2003, 12:55 PM

Quote:

Originally posted by TredWel
I double checked my summation with Maple, and found my error.

Glad I could help.

12-14-2003, 01:33 PM	#6
TredWel High School Varsity Join Date: Oct 2000 Location: Old Forge, PA	Yes, you can expect to win 50 cents by playing this game. I double checked my summation with Maple, and found my error. __________________ There are three things I have learned never to discuss with people...religion, politics, and the Great Pumpkin. - Linus Van Pelt

12-14-2003, 08:35 AM	#2
Katon College Benchwarmer Join Date: Mar 2003 Location: Providence, RI	A little under 40 cents, I'd say. QuikSand, I think you missed that as soon as TredWel wins one the game stops.

12-14-2003, 08:46 AM	#4
QuikSand lolzcat Join Date: Oct 2000 Location: Annapolis, Md	How about 50 cents.

12-14-2003, 09:32 AM	#5
rdo n00b Join Date: Oct 2000 Location: Brisbane	I get the same answer as Quiksand. You expect to lose $0.50. From (1-2x)/(1-x) where x is the probablity of a head.

12-15-2003, 11:40 AM	#7
Wolfpack Pro Rookie Join Date: Feb 2003 Location: Raleigh, NC	So, this is one of those quirky things where expectation could never meet real life, simply because you are playing with whole numbers (winner always gets $1) and the expectation is a fraction (.50).

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