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 Sum crazy dice (Posted on 2006-11-30)
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)

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 my solution to part c wrong | Comment 5 of 8 |
(In reply to re: Solution -- I don't understand part c by Charlie)

You are entirely correct, I misread the problem, although I still don't read it the way you do.  I read it as "not all the same number" but it is clearly "all different" which is different.

I am now reading it as p(all different) > p(sum<=15) and p(all different) < p(sum<=16)

With this reading there is no integer n.

Why?  for n=6 (and lower) the second condition is satisfied but the first is not.
for n=7 (and hight) the first condition is satisfied but the second is not.

I don't really see how to read it as conditional probability.

So what is being asked in part c?

 Posted by Joel on 2006-11-30 16:17:07

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