Let us consider a duodecimal prime number which when re-interpreted as a base ten positive integer is a composite number. As an example, (45)₁₂ is equal to (53)₁₀ and therefore a prime number. However, (45)₁₀ is evidently a composite number.

Determine the probability an integer chosen at random from (100)₁₂ to (BBB)₁₂ inclusively is a prime number in the duodecimal system, but is composite when re-interpreted as a base ten number.