Two cards are drawn simultaneously (or successively without replacement) from a well shuffled pack of 52 cards. Find the mean, variance and standard deviation of the number of kings.

Answer

Mean`=34/221` and Variance`=6800/221` and Standard Deviation`=0.37`

Explanation

Let `X` denote the number of Kings in a draw of two card


`rArr P(X=0)=P(no \ king)=(48C_2)/(52C_2)=(48 times 47)/(52 times 51)=188/221`


`rArr P(X=1)=P("one king and one non king")=(4C_1 times 48C_1)/(52C_2)=(4 times 48)/(52 times 51)=32/221`


`rArr P(X=2)=P("two king")=(4C_2)/(52C_2)=(4 times 3)/(52 times 51)=1/221`


Probability of Distribution:


Mean,`E(X)=sum_(i=2)^n x_i cdot p(x_i)=0 times 188/221+1 times 32/221+2 times 1/221`


`0+32/221+2/221=34/221`


`rArr E(X)=34/221`


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