Q. 55.0( 1 Vote )

# Two cards are dra

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 p_{i} and x_{i.}

Let’s proceed to find mean and standard deviation.

Mean of any probability distribution is given by Mean = ∑x_{i}p_{i}

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

Variance = ∑ x_{i}^{2}p_{i} – (∑x_{i}p_{i})^{2}

∴ first we need to find the products i.e. p_{i}x_{i} and p_{i}x_{i}^{2} 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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