MHT CET · Maths · Probability
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
- A \(\frac{1}{221}\)
- B \(\frac{1}{220}\)
- C \(\frac{3}{220}\)
- D \(\frac{2}{221}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{221}\)
Step-by-step Solution
Detailed explanation
Two cards are drawn from a pack of 52 cards without replacement. Total queen cards are 4
\(\therefore P\left(1^{\text {st }} \text { queen card }\right)=\frac{4}{52} \text { and } P\left(2^{\text {nd }} \text {queen card}\right)\) \(=\frac{3}{51}\)
\(\therefore \text { Required probability }=\frac{4 \times 3}{52 \times 51}=\frac{1}{221}\)
\(\therefore P\left(1^{\text {st }} \text { queen card }\right)=\frac{4}{52} \text { and } P\left(2^{\text {nd }} \text {queen card}\right)\) \(=\frac{3}{51}\)
\(\therefore \text { Required probability }=\frac{4 \times 3}{52 \times 51}=\frac{1}{221}\)
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