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

Correct Answer: Option B

n(S) = \({}^{52}C_2\) = 1326

Let A = event of getting both red cards

and B = event of getting both queens

then \(\left(A\cap B\right)\) = event of getting two red queens

n(A) = \({}^{26}C_2\) = 325, n(B) = \({}^4C_2\) = 6

\(n(A\cap B)={}^2C_2=1\)

\(\therefore\;P\left(A\right)=\frac{325}{1326},\;P\left(B\right)\;=\;\frac6{1326}\)

\(P\left(A\cap B\right)=\frac1{1326}\)

P ( both red or both queens) = \(P\left(A\cup B\right)\)

= \(P\left(A\right)+P\left(B\right)-P\left(A\cap B\right)=\) \(\frac{325}{1326}+\frac1{221}-\frac1{1326}\) = \(\frac{55}{221}\)