Q:

probability of deck of playing cards

If 1 card is drawn from a well-shuffled deck of 52 playing cards, what are the probabilities of getting the following?  

red king 
a black card 
a 3,4,5,or 6 
a diamond 
not a diamond 
not an ace

A:

There are 52 cards in a deck.
The probability of getting something is $\frac{number\ of\ favorable\ cases}{number\ of\ possible\ cases}$

Red king: $\frac{1}{26}$ - there are 2 red kings in 52 cards. So $\frac{2}{52} = \frac{1}{26}$  
A black card: $\frac{1}{2}$. There are 26 black cards from a total of 52. So $\frac{26}{52} = \frac{1}{2}$  
3,4,5 or 6: $\frac{4}{13}$. There are 16 favorable cards (4 of each.) So $\frac{16}{52} = \frac{4}{13}$  
a diamond: $\frac{1}{4}$. There are 13 diamonds in a total of 52. So $\frac{13}{52} = \frac{1}{4}$  
not a diamond:  $\frac{3}{4}$ (1-chance of getting a diamond). So $1 - \frac{1}{4} = \frac{3}{4}$. Or there are 39 cards that are not diamonds. So $\frac{39}{52} = \frac{3}{4}$  
not an ace: $\frac{12}{13}$ - there are 48 cards that are not an ace in a total of 52. So $\frac{48}{52} = \frac{12}{13}$  

