Bob's password consists of a non-negative single-digit number followed by a letter

P (  odd single digit number )  = 

( 5 odd single digits / 10 non-negative single digits)  = (5/10)  = 1/2

 

P (positive single digit number )  = 

(9 positive single digits / 10 non-negative single digits)  = 9/10

 

The total probability is   (1/2) (9/10)  =  9/20

Example: 1A2.

 

You have: 10 choices for 1  x  26 choices for A  x  10 choices for 2 (if repeats are allowed) =2,600 codes.

 

Then: You have 5 choices for ODD number  x  26 choices for the letter  x  4 choices for a prime number=520

 

Therefore, the probability =520 / 2600 =1 / 5