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Two cards are drawn at random from a well - shuffled pack of 52 cards. what is the probability that either both are red or both are queens?

Correct Answer: 55/221

Explanation:

n(S) =  C 2 52  = 1326


 


 Let  A = event of getting both red cards


 


and B = event of getting both queens


 


then  A B  = event of getting two red queens


 


n(A) =  C 2 26  = 325,   n(B) =  C 2 4  = 6


 


  n ( A B ) = C 2 2 = 1


 


    P A = 325 1326 ,   P B   =   6 1326


 


  P A B = 1 1326


 


P ( both red or both queens) =  P A B


 


P A + P B - P A B = 325 1326 + 1 221 - 1 1326 = 55 221


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