"The chance of rolling any given double (e.g., as in your link, a double 6) is indeed 1∕36. There are, however, six doubles to choose from, so the total probability is in fact 1∕6 of rolling any double."
Well when playing the game one is generally attempting to achieve a particular double, so I'll let that stand.
"Alas, adding probabilities does not work that way. In effect you've counted the outcome of a double twice. The chance of rolling at least one of a given number with 2 dice is, in fact, 1−(1−1∕6)²=11∕36."
I did have doubts about adding probabilities like that. However, since the fraction 11/36 is almost a third, doesn't that in effect equate to 1/3?
"The chance of rolling any given double (e.g., as in your link, a double 6) is indeed 1∕36. There are, however, six doubles to choose from, so the total probability is in fact 1∕6 of rolling any double."
Well when playing the game one is generally attempting to achieve a particular double, so I'll let that stand.
"Alas, adding probabilities does not work that way. In effect you've counted the outcome of a double twice. The chance of rolling at least one of a given number with 2 dice is, in fact, 1−(1−1∕6)²=11∕36."
I did have doubts about adding probabilities like that. However, since the fraction 11/36 is almost a third, doesn't that in effect equate to 1/3?