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16 Mar 2021, 02:00
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A
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Difficulty:
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Question Stats:
98% (01:21) correct
2%
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wrong
based on 83
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From a pack of 52 cards, two are drawn one by one without replacement. What is the probability that both of them are jacks ?
A. 1/221
B. 11/850
C. 25/204
D. 5/24
E. 5/21
A. 1/221
B. 11/850
C. 25/204
D. 5/24
E. 5/21
16 Mar 2021, 19:17
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Given: A pack of 52 cards, 2 cards are drawn one by one without replacement.
Probability that both cards are Jack = ?
Probability that first card is Jack = \(\frac{4}{52}\)
After the first cared is removed,
Probability that second card is Jack = \(\frac{3}{51}\) [3 Jacks remaining as first card was Jack]
As both the events are dependent on each other, i.e. second card will be drawn after the first one, the probabilities will get multiplied.
=> Probability that both cards are Jack = \(\frac{4}{52}\) * \(\frac{3}{51}\) = \(\frac{1}{221}\).
So correct answer is option A.
Probability that both cards are Jack = ?
Probability that first card is Jack = \(\frac{4}{52}\)
After the first cared is removed,
Probability that second card is Jack = \(\frac{3}{51}\) [3 Jacks remaining as first card was Jack]
As both the events are dependent on each other, i.e. second card will be drawn after the first one, the probabilities will get multiplied.
=> Probability that both cards are Jack = \(\frac{4}{52}\) * \(\frac{3}{51}\) = \(\frac{1}{221}\).
So correct answer is option A.
