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.

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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