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    Question

    Two cards are drawn at random from a pack of 52 cards.

    What is the probability that either both are black or both are queens?
    A 17/121 Correct Answer Incorrect Answer
    B 55/221 Correct Answer Incorrect Answer
    C 48/521 Correct Answer Incorrect Answer
    D 13/221 Correct Answer Incorrect Answer
    E 17/211 Correct Answer Incorrect Answer

    Solution

    N(S) = 52C2 = 1326 Let A be the event of getting two Black cards And B be the event of getting two queens And (A∩B) be the event of getting two black queens ∴ n(A) = 26C2 , n(B) =4C2 , n(A∩B) = 2C2 ∴ P(A) = 26C2/52C2 ,         P(B)= 4C2/52C2 ,      P(A∩B) = ( 2C2)/52C2 Required Probability = P(A) + P(B) - P(A∩B)  = 26C2/52C2 + 4C2/52C2 - ( 2C2)/52C2 = 325/1326+  1/221+  1/1326 = 55/221          

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