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?
Correct Answer: Option C
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) = \(\frac{52\times51}{2\times1}\) = 26c2 = 325, n(B)= \(\frac{26\times25}{2\times1}\)= 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
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