- #1
royboyz12
- 6
- 0
This seems to be a fairly simple probability question but it's stumping me for some reason.
"You flip a fair coin until you get a head and win x dollars, where x is the number of flips it takes to get a head. (e.g. H = win $1; TH = win $2; TTH = win $3, and so on.) How much should you pay to play this game for it to be equitable (each player's expectation is equal to 0)?"
I'm really not sure if the answer is supposed to be a specific value or a variable, although my guess would be a specific dollar amount. I tried setting up a few equations like (1/2)(x)+(1/2)(L)=0 where x is the dollar amount and L is a lose, but that only gave me L=-x which didn't make any sense to me. I also tried setting it up as a series that produced x=0,-1,-1/2 which didn't seem to make sense either. I feel like I'm making it more complicated than it has to be, but I have no idea what to do.
Anyway, any help would be greatly appreciated. Thanks!
"You flip a fair coin until you get a head and win x dollars, where x is the number of flips it takes to get a head. (e.g. H = win $1; TH = win $2; TTH = win $3, and so on.) How much should you pay to play this game for it to be equitable (each player's expectation is equal to 0)?"
I'm really not sure if the answer is supposed to be a specific value or a variable, although my guess would be a specific dollar amount. I tried setting up a few equations like (1/2)(x)+(1/2)(L)=0 where x is the dollar amount and L is a lose, but that only gave me L=-x which didn't make any sense to me. I also tried setting it up as a series that produced x=0,-1,-1/2 which didn't seem to make sense either. I feel like I'm making it more complicated than it has to be, but I have no idea what to do.
Anyway, any help would be greatly appreciated. Thanks!