Question 309447
Prime numbers from 1 to 20 are 
2, 3, 5, 7, 11, 13, 17, 19  
The number 1 is neither prime nor composite (if your teacher doesn't feel that way then modify as necessary).
That makes 8 numbers prime.  
11 numbers composite.
1 special number (the number 1).
20 total.
P(prime)=8/20=2/5
Without replacement the total number of cards drops to 19.
P(composite)=11/19
P(prime, composite)=(2/5)(11/19)=22/95