Three cards are drawn successively with replacement from a well-shuffled deck of 52 cards. A random variable X denotes the number of spades in three cards. Determine the probability distribution of X.

 Let X denote the number of doublets. X can take the value 0, 1, 2, or 3.
Possible doublets are (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)

Probability of getting a doublet  = 

Probability of not getting a doublet  = 

Now,   P(X = 0) = P(no doublet) = 

           

           
and 
                         
∴ the required probability distribution is