# Probability. You roll, I roll game.

1. Apr 6, 2012

### bizboy1

1. The problem statement, all variables and given/known data
You roll a die, and I roll a die. You win if the number showing on your die is strictly greater than the one on mine. If we play this game five times, what is the chance that you win at least four times? The answer is .1005

2. Related Equations[\b]
Binomial

3. The attempt at a solution
I haven't got anywhere.
I know the game looks something like this:
ffs
fffs
ffffs
fffffs
blacks

and I found all 15 pairs to win. I'm just not sure how I should think about it. This is not for homework. I am reviewing probability. Thanks!!!

Last edited: Apr 6, 2012
2. Apr 6, 2012

### bizboy1

I think I figured it out. The problem with me and these questions is that I read them wrong/differently. Anyone else confused by the five games?

3. Apr 6, 2012

### Dick

Try warming up by finding the probability if the game is played only once.

4. Apr 6, 2012

### bizboy1

I got it. The trick was applying the binomial theorem to the wins and not to the individual rolls.

5. Apr 6, 2012

### Dick

I was confused by trying to respond to this problem and trying to figure out what to do with "I" and "you". The five games part wasn't particularly confusing.

6. Apr 6, 2012

### bizboy1

Answer: Probability of a win is 15/36. Now then use binomial(5,4)*(15/36)^4*(21/36)+binomial(5,5)*(15/36)^5

7. Apr 6, 2012

### bizboy1

My confusion was the word play. Play means exactly what? 5 rolls total? That doesn't make sense. So it must be 5 complete games. Game includes the complete description.

8. Apr 6, 2012

Sure it is.

9. Apr 7, 2012

### Ray Vickson

The wording is ambiguous: you say "You win if the number showing on your die is strictly greater than the one on mine". Does that mean that I win if my number is >= yours? (Another interpretation would be: you win if your number is larger, I win if my number is larger and we toss again if both numbers are equal. In that case, we each have a 1/2 chance to win in each play of the game---where 1 play means we keep tossing until someone wins.)

RGV