A base ten positive integer is called a Matched Number if each of the respective sod’s in their duodecimal and hexadecimal representations is a prime number, where sod(x) represents the sum of the digits of x.

For example, 73 (base ten) is equal to 61 in the duodecimal system and, 49 in the hexadecimal system. Hence, 73 (base ten) is a Matched Number since each of the sods of 61_{12} and 49_{16} considered in their respective bases, is a prime number.

Determine the probability that X is a Matched Number, given that X is a positive integer drawn at random between 100 (base ten) and 9999 (base ten) inclusively.