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

#### acevipa

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.

#### SpringFan25

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?

acevipa

#### acevipa

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?