The probability is 1.  Since 2 is the one and only even prime number, all the
rest are odd.  So it is absolutely certain that if you chose one of the prime 
numbers between 100 and 200, it will be odd.  Here are all 21 prime numbers
between 100 and 200, and they are all odd:

101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 
151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199.

The probability is 21 ways out of 21, and  = 1.

Edwin