Roland Bones tosses a pair of dice. What are the odds that he won't roll a $2,3,7,11,$ or $12$.
I will quietly put this out there that I have two interpretations of this problem mainly because of the phrase "pair of dice." The results $2,3,7,11$ or $12$ either mean the sum of the results rolled or simply possible outcomes on either of the two dice; in other words, a dice "could roll" a $2,3,7,11,12$.
The first case can easily be solved by listing all the cases. The probability of the attaining the undesired numbers as a sum of two numbers is $\frac{1}{3}$. So the probability of not getting one of these numbers is $\frac{2}{3}$ or an odds of $2:1$.
Two questions (or one if you bash out the first): Is the second interpretation possible? If so, what are the odds of rolling $2$ such that the a number doesn't roll a $2,3,7,11,$ or $12$?