All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Probability
Sum crazy dice (Posted on 2006-11-30) Difficulty: 3 of 5
a) I have a pair of fair n-sided dice. The probability when both are rolled that their results differ by two is the same as that the sum will be 5 or less. Find n.

b) I have two dice, one with n sides and the other with m sides. When they are rolled the probability they are equal is the same as that they sum to 13 or higher. Find n and m.

c) I have a trio of n-sided dice. When I roll them all the probability that the dice all show different numbers is greater than when they sum 15 or less but less than when they sum 16 or less. Find n.

Note: "x sided dice" are numbered with consecutive integers from 1 to x.

No Solution Yet Submitted by Jer    
Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Solution -- I don't understand part c | Comment 4 of 8 |
(In reply to Solution by Joel)

With three 6-sided dice the probability that all the dice are different is 5/9, or .5555555555555556. When the dice sum 15 or less, that probability is .5825242718446602 and when the dice sum 16 or less it's .5660377358490566.

The best that I can come up with is for n=10

10            0.7200000000 0.7058823529 0.7200000000

where the probability of getting all three different is 0.72, but when the dice sum 15 or less, that probability is 0.70588..., and when 16 or less, its the same 0.72 as the unconditional probability.

 


  Posted by Charlie on 2006-11-30 14:49:04
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (9)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information