Two cards are drawn at random from a pack of 52 cards what is the probability that either both are b......

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