Probability. You roll, I roll game.

In summary: If we play this game five times, what is the chance that you win at least four times? The answer is .1005
  • #1
bizboy1
11
0

Homework Statement


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

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:
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  • #2
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
Try warming up by finding the probability if the game is played only once.
 
  • #4
I got it. The trick was applying the binomial theorem to the wins and not to the individual rolls.
 
  • #5
bizboy1 said:
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?

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
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
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
bizboy1 said:
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

Sure it is.
 
  • #9
bizboy1 said:

Homework Statement


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

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!


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
 

1. What is the "Probability: You roll, I roll game?"

The "Probability: You roll, I roll game" is a game that involves two players rolling a die, with each player trying to guess the outcome of the other player's roll. The player who guesses the correct outcome earns a point, and the player with the most points at the end of the game wins.

2. How do you calculate the probability of winning in this game?

The probability of winning in this game depends on the number of players and the number of rounds played. Generally, the more players involved and the more rounds played, the lower the probability of winning for any individual player.

3. Is this game based purely on luck?

The outcome of each roll in this game is determined by chance, but players can use strategies and probability calculations to increase their chances of winning. So while luck plays a role, there is also an element of skill involved in this game.

4. Can you use mathematical formulas to predict the outcome of this game?

Yes, there are mathematical formulas and strategies that can help players make more accurate predictions in this game. However, these formulas cannot guarantee a win as the outcome of each roll is ultimately determined by chance.

5. How does the concept of probability apply to real-life situations?

Probability is used in various real-life situations, such as predicting the outcome of a sports game or the likelihood of a certain event occurring. It helps us make informed decisions and understand the likelihood of different outcomes.

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