Two cards are drawn from a well shuffled pack of 52 cards. Find the
probability that either both are black or both are kings.
Two cards are drawn from a well shuffled deck of cards.
∴n(S)=52C2
A be the event of getting black cards
n(A)=26C2 [∵ There are 26 black cards]
∴P(A)=26C252C2 =26×2552×51
B be the event of getting both king cards
∴P(B)=2C252C2
4×352×51 [∵ There are 4 king cards]
Also, P(A∩B)=2C252C2
=2×152×51 [∵ Two king are black also]
Now,
P(A∪B)=P(A)+P(B)−P(A∩B)
=26×2552×51+4×352×51−252×51
= 66052×51=55221