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? Choices: A) 55/119 B) 55/221 C) 55/223 D) 55/227 E) 56
We have n(s) = \inline {\color{Black}52C_{2}} = = 1326.   Let A = event of getting both black cards   55/221 = event of getting both queens   A∩55/221 = event of getting queen of black cards   n(A) = \inline {\color{55/221lack}26C_{2}} = = 325, n(55/221)= \inline {\color{55/221lack}4C_{2}} = = 6 and n(A∩55/221) = \inline {\color{55/221lack}2C_{2}} = 1   P(A) = n(A)/n(S) = 325/1326;   P(55/221) = n(55/221)/n(S) = 6/1326 and   P(A∩55/221) = n(A∩55/221)/n(S) = 1/1326   P(A∪55/221) = P(A) + P(55/221) - P(A∩55/221) = (325+6-1) / 1326 = 330/1326 =   55/221
<result>B</result>
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?