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?
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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