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23 Aug 2017, 09:30
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Two cards are drawn at random from pack of 52 cards , what's the probability that either both are black or both are queens?
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IshpalSingh
Joined: 10 Dec 2015
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Concentration: Strategy, Finance
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23 Aug 2017, 09:48
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We have n(s) = 52C2= 1326.
Let A = event of getting both black cards
B = event of getting both queens
A∩B = event of getting queen of black cards
n(A) = 26C2 = 325, n(B)= 4C2 = 6 and n(A∩B) = 2C2 = 1
P(A) = n(A)/n(S) = 325/1326;
P(B) = n(B)/n(S) = 6/1326 and
P(A∩B) = n(A∩B)/n(S) = 1/1326
P(A∪B) = P(A) + P(B) - P(A∩B) = 55/221
Let A = event of getting both black cards
B = event of getting both queens
A∩B = event of getting queen of black cards
n(A) = 26C2 = 325, n(B)= 4C2 = 6 and n(A∩B) = 2C2 = 1
P(A) = n(A)/n(S) = 325/1326;
P(B) = n(B)/n(S) = 6/1326 and
P(A∩B) = n(A∩B)/n(S) = 1/1326
P(A∪B) = P(A) + P(B) - P(A∩B) = 55/221
