Probability of dice landing on '6' for 3rd time on the 20th roll

Feb 2008
297
7
A die is rolled repeatedly:

1) Find the probability that the 3rd time a '6' shows is on the 20th role.

2) Generalise to the kth time on the nth roll.
 
May 2010
1,034
272
you are bing asked to derive a standard distribution, but i cant remember the name of the thing.

anyway, Here is a hint to get you started

part (a)
Find the chance that there are 2 sixes on the first 19 rolls, and multiply by the chance of getting a 6 on the 20'th roll.

You can get the probability of 2 6's in 19 rolls by using the bonomial distribution.


part (b)
The above argument generalises.



Can you finish from there?
 
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Feb 2008
297
7
you are bing asked to derive a standard distribution, but i cant remember the name of the thing.

anyway, Here is a hint to get you started

part (a)
Find the chance that there are 2 sixes on the first 19 rolls, and multiply by the chance of getting a 6 on the 20'th roll.

You can get the probability of 2 6's in 19 rolls by using the bonomial distribution.


part (b)
The above argument generalises.



Can you finish from there?
Yeah thanks. I managed to get the answer with your help.