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.

(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