Rolling 2d6, there are 36 possible outcomes in the range [2..12].

1). Let's say I choose the range [2..10] as success, what then is my confidence? There is only one way to get a 12 and two ways to get an 11, for 3/36 of the outcomes, so my confidence in success is 33/36.

2). Let's say I choose 30/36 as my confidence, what then is the matching range? There are three ways to get a 10 + 2 elevens + 1 twelve = 6/36, so my range in order to achieve that level of confidence is [2..9].

How can I more formally determine a range given a confidence or a confidence given a range?

1). Let's say I choose the range [2..10] as success, what then is my confidence? There is only one way to get a 12 and two ways to get an 11, for 3/36 of the outcomes, so my confidence in success is 33/36.

2). Let's say I choose 30/36 as my confidence, what then is the matching range? There are three ways to get a 10 + 2 elevens + 1 twelve = 6/36, so my range in order to achieve that level of confidence is [2..9].

How can I more formally determine a range given a confidence or a confidence given a range?

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