In a deck of 52 cards there are 4 kings each of one suit respectively.

Let X be the random variable denoting the number of kings for an event when two cards are drawn simultaneously.

∴ X can take values 0 , 1 or 2.

P(X=0) =

[For selecting 0 kings, we removed all 4 kings from deck and selected out of 48]

P(X=1) =

[For selecting 1 king, we need to select and 1 out of 4 and not any other]

P(X=2) =

[For selecting 2 king, we need to select and 2 out of 4]

Now we have p_i and x_i.

Let’s proceed to find mean and standard deviation.

Mean of any probability distribution is given by Mean = ∑x_ip_i

Standard Deviation is given by SD = √ Variance where variance is given by:

Variance = ∑ x_i²p_i – (∑x_ip_i)²

∴ first we need to find the products i.e. p_ix_i and p_ix_i² and add them to get mean and apply the above formula to get the variance.

Following table gives the required products :

∴ mean =

Variance =

∴ Standard deviation = √variance = √(400/2873)

=