Math Is Fun Forum

pokerhermit

Member

Registered: 2008-01-26

Posts: 2

Dice Probability question?

You throw a die and write down the numbers until you have rolled every number at least once. On average, how many rolls until you have marked down every number?

I think the answer is 14.7.

I don't know how to write it as a formula but the basic idea is: Sum  6/6..6/1

If that's right, can you get an average of how many numbers you have marked down by your nth roll?

pokerhermit

Member

Registered: 2008-01-26

Posts: 2

Re: Dice Probability question?

I don't know if there is some equation for this problem, but I wrote an algorithm to solve it instead.

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Dice Probability question?

after going through a bit of figuring things out, i've came up with an expression for the probability of it taking 'n' number of rolls, however im not sure how to expand it, or even write it out properly in the first place, so ill give examples going down the line

i've tested it out in a program, computing the values experimentally and analytically, and it does seem to be prefectly correct, so if you can get an expression for P(n) then you can use that to get an exact equation for the average number of rolls

and yes, 14.7 is the answer (the exact answer in fact, the sum nP(n) converges prefectly to 14.7 (atleast after many iterations i had 14.699998... and it is just far too slow executing at large values of n for p(n) to withstand ;P))

Last edited by luca-deltodesco (2008-02-01 03:17:54)

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luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Dice Probability question?

infact, it should be that this will work for an 'm' sided die.

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