Q. 16

Two cards are drawn without replacement from a well-shuffled deck of 52 cards. Let X be the number of face cards drawn. Find the mean and variance of X.

Answer :

Given : Two cards are drawn without replacement from a well-shuffled deck of 52 cards.


To find : mean (𝓊) and variance (σ2) of X


Formula used :



Mean = E(X) =


Variance = E(X2) -


Mean = E(X) = = x1P(x1) + x2P(x2) + x3P(x3)


Two cards are drawn without replacement from a well-shuffled deck of 52 cards.


Let X denote the number of face cards drawn


There are 12 face cards present in 52 cards


P(0) = = =


P(1) = = =


P(2) = = =


The probability distribution table is as follows,



Mean = E(X) = 0() + 1() + 2() = 0 + + = = =


Mean = E(X) =


= =


E(X2) = = P(x1) + P(x2) + P(x3)


E(X2) = () + () + () = 0 + + =


E(X2) =


Variance = E(X2) - = = =


Variance = E(X2) - =


Mean = E(X) =


Variance =


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