Two cards are drawn at random from a well - shuffled pack of 52 cards. what is t

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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?
Options
A. 17/112
B. 55/221
C. 55/121
D. 33/221

Correct Answer

55/221

Explanation

n(S) = ${}^{52}C_{2}$ = 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) = ${}^{26}C_{2}$ = 325, n(B) = ${}^{4}C_{2}$ = 6

$n (A ? B) = {}^{2}C_{2} = 1$

$? P (A) = \frac{325}{1326}, P (B) = \frac{6}{1326}$

$P (A ? B) = \frac{1}{1326}$

$?$ P ( both red or both queens) = $P (A ? B)$

= $P (A) + P (B) - P (A ? B) =$ $\frac{325}{1326} + \frac{1}{221} - \frac{1}{1326}$ = $\frac{55}{221}$