Question

Two cards are drawn at random from a well - shuffled pack of 52 cards. what is the probability that either both are red or both are queens?

A) 17/112 B) 55/221 C) 55/121 D) 33/221

Answer 1

Answer:

option (b) is correct 55/221

Step-by-step explanation:

n(S) = C252 = 1326

Let A = event of getting both red cards

and B = event of getting both queens

then (A∩B) = event of getting two red queens

n(A) = C226 = 325, n(B) = C24 = 6

n(A∩B)=C22=1

∴ P(A)=325/1326, P(B) = 6/1326

P(A∩B)=1/1326

∴P ( both red or both queens) = P(A∪B)

= P(A)+P(B)−P(A∩B)=325/1326+1/221−1/1326=55/221