Two cards are drawn from a pack of well shuffled 52 playing cards one by one without replacement. Then the…

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
  1. $\frac{1}{221}$
  2. $\frac{1}{220}$
  3. $\frac{3}{220}$
  4. $\frac{2}{221}$

Solution

Two cards are drawn from a pack of 52 cards without replacement. Total queen cards are 4 $\begin{array}{l} \therefore P\left(1^{\text {st }} \text { queen card }\right)=\frac{4}{52} \text { and } P\left(2^{\text {nd }} \text { queen card }\right)=\frac{3}{51} \\ \therefore \text { Required probability }=\frac{4 \times 3}{52 \times 51}=\frac{1}{221} \end{array}$

Asked in: MHT CET 2020 (12 Oct Shift 1)

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