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#1 2005-08-09 23:54:33

Maxi
Guest

Probability of Winning on a Dice Game

I need to work out the probability of winning the following dice game.  Can anybody help? I've got myself into a state of confusion.

THE GAME
----------
- You have two dice with numbers 1-6.
- The dealer will roll the dice and get 2 numbers - say 5 and 2
- The player must then try and get the same numbers in either 1 or 2 rolls.
- If they get one of the numbers in the first roll, they only have to roll the   other dice in the second roll.
- The ways that they could win is either both in the first roll, one on each roll, or both in the second roll.

I think that the chance of winning is 1/9.  What is the probability that you get?

#2 2005-08-10 00:15:36

mathsyperson
Moderator

Offline

Re: Probability of Winning on a Dice Game

There are two basic forms that the dealer could throw: a, a or a, b. His chance of getting a, a is 1/6 and of getting a, b is 5/6.
Consider a, a first. Let's say he threw two 6's. So the player could throw two sixes first (1/36) or one six then another six (10/36*1/6) or no sixes then two sixes (25/36*1/36) Adding these possibilities gives 121/1296. The dealer had a 1/6 chance of getting the a, a form, so the total probability would be 121/7776.

Now a, b. Say the dealer threw 6, 5. The player could throw 6, 5 or 5, 6 first (2*1/36) or 6 first then 5 or 5 first then 6 (2*9/36*1/6) or throw neither first and both second (16/36*2*1/36). Adding these gives 53/324, but the dealer had a 5/6 chance of getting this so the total chance would be 265/1944.

The chance of winning the whole game is therefore 121/7776+265/1944, which is 1181/7776. I think...


Why did the vector cross the road?
It wanted to be normal.

#3 2005-08-10 00:29:07

Maxi
Guest

Re: Probability of Winning on a Dice Game

I've just done this work, is any of it right lol?


To win: dice A = 5 B = 2
        dice A = 2 B = 5

The probability of doing this in one roll is:
     A = 5 is 1/6 AND B = 2 is 1/6 so 1/36
OR
     A = 2 is 1/6 AND B = 5 is 1/6 so 1/36
So probability of doing it in one roll one roll is 1/18

The probobility of doing it in two rolls is:
     A = 5 is 1/6 OR  B = 2 is 1/6 so 2/6
AND  Other Dice = 5/2 (depending on previous number) is 1/6
so probability of doing it in two rolls is also 1/18

So the probability of winning is 1/18

#4 2005-08-10 00:31:06

Maxi
Guest

Re: Probability of Winning on a Dice Game

Mathsyperson...you've totally lost me lol

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