We have total 26 red cards in a deck of 52 cards.

As we are drawing maximum 3 cards at a time so we can get maximum 3 red cards.

If X denotes the number of red cards ,then X can take values from 0,1,2 and 3

P(X=0) = probability of drawing no red cards

We need to select all 3 cards from remaining 26 cards

Total possible ways of selecting 3 cards =

∴ P(X=0) =

P(X=1) = P(selecting one red and 2 black cards) =

P(X=2) = P(selecting 2 red and 1 black cards) =

P(X=3) =

So, Probability distribution is given below:

Mean =