# The Dice Game

• Mar 13th 2013, 01:32 AM
atomicdog5555
The Dice Game
Jack and Jill play a dice game where they roll a die. Jack wins if the number he rolls is higher than Jill's. Jill wins if the number she rolls is higher than Jack's. If both of them roll the same number, Jill wins.

a) Jack rolls his die twice and notes the higher of the two numbers while Jill only rolls her die once. What is the probability that Jack will win?
b) Find a general formula for the probability that Jack will win if both Jack and Jill roll the die multiple times and note the highest number rolled
• Mar 13th 2013, 05:58 AM
Plato
Re: The Di
Quote:

Originally Posted by atomicdog5555
Jack and Jill play a dice game where they roll a die. Jack wins if the number he rolls is higher than Jill's. Jill wins if the number she rolls is higher than Jack's. If both of them roll the same number, Jill wins.
a) Jack rolls his die twice and notes the higher of the two numbers while Jill only rolls her die once. What is the probability that Jack will win?
b) Find a general formula for the probability that Jack will win if both Jack and Jill roll the die multiple times and note the highest number rolled

There are thirty-six pairs that result from rolling a die twice.
In fifteen of them the first term is greater than the second term.

In twenty-one of them the second term is at least as large than the first term.
• Mar 13th 2013, 06:10 AM
Shakarri
Re: The Dice Game
These problems are normally done by drawing a table with all the results in it rather than calculating the answer directly.
• Mar 13th 2013, 11:06 PM
atomicdog5555
Re: The Di
Just a quick question: How many ways are there to throw 4 die such that the highest number obtained is "six"? I know the first way of doing this is to take (6^4) - (5^4). Is there another way? Thanks so much
• Mar 14th 2013, 04:45 AM
Shakarri
Re: The Dice Game
[chance of throwing one ore more sixes]= 1- [chance of not throwing a six]

Once you have the chance of throwing one or more sixes, multiply it by the total number of ways to throw the dice $(6^4)$