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) = $\frac{52*51}{2*1}$ =  $26C2$ = 325, n(B)= $\frac{26*25}{2*1}$= 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