# Probability of succesful rolls of different sided dies

This seems so simple, but I'm not sure how to calculate it.

I have one six-sided die and one 12-sided die.

What is the probability that, on a roll of both dice, that the six-sided die will win?

I'm not overly familiar with mathematical notation. Thank you!

• Just one poor little six-sided? I assume wins means greater. Then the probability is $(1/6)(0/12)+(1/6)(1/12)+(1/6)(2/12)+(1/6)(3/12)+(1/6)(4/12)+(1/6)(5/12)$. This simplifies to $5/24$. – André Nicolas Apr 14 '15 at 9:16
• Similarly, the probability of a tie is $6(1/6)(1/12)=2/24$ and the probability of a loss is $17/24$, so if you roll again after a tie then the probability of the six-sided die eventually winning is $5/22$ – Henry May 14 '15 at 19:09