Thread: Regarding Dice

This might be simple but for some reason I can not stop pondering this question....
Is the probability of rolling 6 dice and getting exactly one 1 equal to the probability of rolling 12 dice and getting exactly two 1s? Please explain thanks.

Originally Posted by tobeelijah1

This might be simple but for some reason I can not stop pondering this question....
Is the probability of rolling 6 dice and getting exactly one 1 equal to the probability of rolling 12 dice and getting exactly two 1s? Please explain thanks.

NO
P(one 1 out of 6 throws) =6(1/6)(5/6)^5 (the 6 comes because the 1 could be 1st 2nd........or6th)
P(two 1s out of 12 throws)= 12C2 (1/6)^2(5/6)^10 (12c2 is the number of different ways two 1s can occur in 12 throws. Actually=66)

How would this change with say 6 six sided dice vs 6 twelve sided dice? In the 6 12 sided dice scenario I would have a 1/6th chance to roll a one or a two right. Therefore the probability would be the same of rolling exactly one 1 or 2?