# Thread: probability of winning after 50 rounds

1. ## probability of winning after 50 rounds

A die is rolled and you are paid $9 when it shows 6 dots, but you have to pay$5 when it shows 1 or 2 dots. You play 50 rounds of this game. What
is the probability of winning (overall) some money.

a hint was given: construct the probability generating function of your total net win

but im having a hard time getting anywhere at all

2. Originally Posted by chrisc
A die is rolled and you are paid $9 when it shows 6 dots, but you have to pay$5 when it shows 1 or 2 dots. You play 50 rounds of this game. What
is the probability of winning (overall) some money.

a hint was given: construct the probability generating function of your total net win

but im having a hard time getting anywhere at all
Here's a start:

Let X be the random variable winnings in a single game.

Pr(X = -5) = 2/6, Pr(X = 0) = 1/2, Pr(X = 9) = 1/6.

Define $\displaystyle Y = X_1 + X_2 + \, .... + X_{50}$ where the $\displaystyle X_i$ are i.i.d. random variables with distribution given above.

You need to calculate Pr(Y > 0).

3. ah good, im going to give this a try and ill report back