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6
Q:

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:   B) 55/221



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

 

 ∴ PA=3251326, PB = 61326

 

 PA∩B=11326

 

∴P ( both red or both queens) = PA∪B

 

= PA+PB-PA∩B=3251326+1221-11326=55221

Subject: Probability
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