Answer :

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 pi and xi.

Let’s proceed to find mean and standard deviation.

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

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

Variance = ∑ xi2pi – (∑xipi)2

first we need to find the products i.e. pixi and pixi2 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)


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