Two cards are drawn simultaneously (without replacement) from a well-shuffled pack of 52 cards. Find the mean and variance of the number of red cards.

We know that in a deck of 52 cards there are 26 red cards and 26 black cards.

Let X be the random variable associated with this experiment of drawing of red cards simultaneously.

∴ X can take values 0 ,1 or 2.

P(X = 0) = Probability of getting 0 number of red card

This means both cards drawn are black.

∴ P(X=0) =

Probability of getting 1 red card and the other non – red = P (X = 1)

P(X = 1) =

P (X =2) = Probability of getting 2 red cards

P(X = 2) =

Probability distribution table for the above random experiment is –

Mean = ∑p_ix_i

Mean = + +

Mean = 1

Variance = ∑p_ix_i² - Mean²

Variance = + + - 1²

∴ variance = 0.49

Mean = 1 & Variance = 0.49.