Three cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find the probability distribution of the number of spades. Hence find the mean of the distribution.

0 spades
1 spades
2 spades
3 spades
Total
(39/52)×(39/52)×(39/52) = 27027/140608
3×(13/52)×(39/52)×(39/52) = 27027/140608
3×(13/52)×(13/52)×(39/52) = 9643/140608
(13/52)×(13/52)×(13/52) = 169/140608
27027+27027+9643+169 = 6464/140608 = 1

The probability of getting a spade remains the same in every pick because the cards are replaced after each pick thus making the picks independent events.
The mean of the distribution is ΣxiP(X=xi) = 3/4.