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Two cards are drawn at random from a pack of 52 cards.what is the probability that either both are black or both are queen?
We have n(s) =52C2
52 = 52*51/2*1= 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) = 52*5/12*1
= 26C2 = 325, n(B)= 26*2/52*1= 4*3/2*1= 6 and n(A∩B) = 4C2 = 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) = (325+6-1) / 1326 = 330/1326 = 55/221
By: Amit Kumar ProfileResourcesReport error
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