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Two cards are drawn from a pack of well shuffled 52 playing cards one by one without replacement. Then the probability that both cards are queens is
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The correct answer is:
$\frac{1}{221}$
Two cards are drawn from a pack of 52 cards without replacement. Total queen cards are 4
$\begin{array}{l}
\therefore P\left(1^{\text {st }} \text { queen card }\right)=\frac{4}{52} \text { and } P\left(2^{\text {nd }} \text { queen card }\right)=\frac{3}{51} \\
\therefore \text { Required probability }=\frac{4 \times 3}{52 \times 51}=\frac{1}{221}
\end{array}$
$\begin{array}{l}
\therefore P\left(1^{\text {st }} \text { queen card }\right)=\frac{4}{52} \text { and } P\left(2^{\text {nd }} \text { queen card }\right)=\frac{3}{51} \\
\therefore \text { Required probability }=\frac{4 \times 3}{52 \times 51}=\frac{1}{221}
\end{array}$
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