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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 ∴ P(A) = 26C2 , P(B) = 4C2 , P(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 + 6/1326 + 1/1326 = 330/1326= 55/221

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