Question

A die is rolled 12 times. Find the chance that the face with six spots appears once among the first 6 rolls, and once among the next 6 rolls.

Answer 1

Pr(6 )=(1/6)*6*(5/6)^5 which is the probability of getting a six in the first six rolls( there are six ways to do it, that accounts for the 6.
The same probability for the next six rolls, so

Pr(6,6)=((1/6)*6*(5/6)^5 )^2=(5/6)^10=.161

So there is a .161 probability of getting one six in the first six rolls, and a six in the second six rolls.