Q. 223.7( 3 Votes )

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.

Answer :

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 = ∑pixi


Mean = + +


Mean = 1


Variance = ∑pixi2 - Mean2


Variance = + + - 12


variance = 0.49


Mean = 1 & Variance = 0.49.


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