Originally Posted by
OneHitWonder
Simple, and the answer to this exercise.
"At least one of the dice is a 2" - the same as "one or more of the dice is a 2" - is not the same as "one or the other die is a 2".
You require "one or the other die is a 2" for the answer of 1/11 chance of 2-2, and the correctly (assumed) inclusive or. This follows from the individual rolls allowed by the question's set of distinctly possible rolls (of "one or the other die is a 2"). Each roll would be roll1 or roll2 or roll3 or... of said set.
A roll of non-2 with 2 doesn't conform to "one or more of the dice is a 2" because there isn't the "... or more of the dice is a 2" possibility then. Wouldn't it be deceptive of a lottery to advertise "one prize or more" were there known to be only one prize from the outset? Like claiming the total prize money is "$X or more" when there's only $X. To state this as clearly as possible, the assertion "two or more of the (two) dice are 2's" is silly. You can't just tack on "or more" when no more possible, or "one" when the "or more" part of the condition has already been fulfilled.