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 Posted: Fri May 18, 2007 7:00 am
Consider a game played with dice. Each of the two players rolls a fair, four-sided dice. What is the probability that Player A scores the maximum X of the two dice while Player B scoress the minimum Y of the two dice?
First, I just want to clarify an understanding of the maximum and minimum. If maximum means the highest number in a set and minimum is the lowest number in a set, the result (for example Player A gets 1,Player B gets 1) would make Player A's maximum equal to the minimum of Player B. Is there any other definition of maximum/minimum that would make maximum=minimun not true?
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Posted: Sat May 19, 2007 1:00 pm
So are you asking for player A to be greater than or equal to player B?
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Posted: Sat May 19, 2007 8:17 pm
By definition of maximum, yes.
But in practical terms, for example, a tennis game where Player A has 2 points and Player B has two points, would it be logical to even think of maximum or minimum? I mean, wouldn't Player B complain if they claim Player A highest scorer (maximum) while they claim Player B to be lowest score (minimum) because in reality, they are both the highest scorer (or lowest scorer depending on how you view it)?
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Posted: Sun May 20, 2007 5:59 am
So... you want A to be greater than B? Because this maximum, minimum thing has me a bit confused. neutral
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Posted: Sun May 20, 2007 6:03 am
Actually, that is my problem. I am not sure wether to consider the maximum as A greater than or equal to B, OR rather simply consider A greater than B because of the fact that it is a game. You just don't want to be called the lowest scorer if your score is the same as the highest scorer, right?
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Posted: Mon May 21, 2007 2:40 pm
Okay, here's what I say then:
Rather than maximum and minimum, we say that player A must be the winner AND player B must be the loser. That way, A might be considered a winner if they have the same, but B isn't a loser, therefore any ties aren't okay.
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Posted: Thu May 24, 2007 4:52 pm
Firstly, are they each rolling one die or a pair of dice?
if the former is correct, then there is a 1/28 chance of player A rolling 4 and player B rolling 1 at the same time, because:
C (n, r) = n! / r! * (n-r)! = number of possible combinations
n = total number of objects
r = number of objects to be selected
8! / (2! * 6!) = 40320 / 1440 = 28
if the latter is correct there is a 1/1820 chance of player A rolling (4, 4) and player B rolling (1, 1):
16! / 4! * (16-4)! = 20922789888000 / 24*479001600 = 1820
and secondly, is this what you are asking?
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Posted: Fri May 25, 2007 3:09 am
According to the problem, each player rolls a die.
So Player A gets one roll, Player B gets one roll. For that one set of rolls Player A gets maximum, while Player B gets the minimum.
You made a mistake in your use of combination because there is at most 4^2=16 possible combination for a pair of four sided dice.
Using combination, there are [C(4,1)]*[C(4,1)] combinations. Note that you never had 8 objects because each die is separate. Each die has four choices, among them, one comes out.
Let's just take it into two cases.
1. Player A scores X greater than or equal to Y (Player B's score). Find the probability of X, and probability of Y.
2. Player A scores X greater than Y (Player B's score). Find the probability of X, and the probability of Y.
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Posted: Thu May 31, 2007 8:52 pm
.....I must have been very, very, tired when I posted... xp sweatdrop
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Posted: Wed Jun 06, 2007 5:41 pm
*sorry I've been off a while*
Okay, here's the answers (I think... :/)
X>/=Y: 10/15 (probability)
X>Y: 6/15 (probability)
But honestly, I just counted up possibilities. sweatdrop I can't remember probability lessons from school with equations for some reason... >.<
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