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08 Jan 2025, 01:30
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
47% (02:26) correct
53%
(01:55)
wrong
based on 133
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A card is randomly drawn from a standard pack of 52 cards without replacement. Is the card a face card?
(1) The probability of drawing two Tens from the remaining 51 cards is 1/425
(2) The probability of drawing two Queens from the remaining 51 cards is 2/425
(1) The probability of drawing two Tens from the remaining 51 cards is 1/425
(2) The probability of drawing two Queens from the remaining 51 cards is 2/425
08 Jan 2025, 05:25
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Bunuel
Is the card a face card?
We should be able to accurately answer if the card drawn is a non-face card or face card based on the information given.
Statement 1 => P = 1/425
If 4 Tens cards would be present in the remaining deck of 51, then probability should have been = 4*3/51*50 = 2/425. As the given probability is less than that, it means that the card already drawn is a Tens card. So we can accurately answer the question as No, hence, the statement is sufficient.
Statement 2 => P = 2/425
As we earlier calculated for Tens cards, similar probability logic holds true, which means that the card drawn initially is not a Queens card as all 4 Queens cards are still in the deck. In this case we cannot comment about other face cards ie. First card drawn could have been King/Jack/Ace or any numbered card. As we cannot accurately answer the question, this statement is insufficient.
IMO: A
08 Jan 2025, 08:32
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Statement (1):
"The probability of drawing two Tens from the remaining 51 cards is
1/425
After drawing one card, there are 51 cards left in the deck. If the first card drawn is a Ten, there are 3 Tens left in the deck of 51 cards. The probability of drawing two Tens from the remaining 51 cards is:
P(Two Tens)=
Number of ways to choose 2 Tens from 3 / Number of ways to choose 2 cards from 51
= 3C2 / 51C2 = 3/(51×50/2) = 3/1275 = 1/425
This matches the given probability. Therefore, the first card drawn must have been a Ten.
Statement (2):
"The probability of drawing two Queens from the remaining 51 cards is
2/425
After drawing one card, there are 51 cards left in the deck. If the first card drawn is a Queen, there are 3 Queens left in the deck of 51 cards. The probability of drawing two Queens from the remaining 51 cards is:
P(Two Queens)= 3C2 / 51C2 = 3/1275 = 1/425
However, the given probability is
2/425
This suggests that the card drawn is not a Queen since drawing a Queen and then two Queens would not give this probability.
To get 2/425 , the calculation must consider a different scenario.
If the first card drawn was not a Queen but a different face card (King or Jack), then the probability of drawing two Queens from the remaining 51 cards would be different. Let's assume the card drawn was not a face card. If the card drawn was a non-face card, the probability of drawing two Queens would be:
P(Two Queens)= 4C2 / 51C2= 6/1275 = 2/425
This matches the given probability. Therefore, the card drawn is not a Queen, but a non-face card.
Conclusion:
Statement (1) alone tells us the card drawn is a Ten, which is not a face card.
Statement (2) alone tells us the card drawn is not a Queen, but it could be a non-face card.
Both statements together confirm that the card drawn is not a face card.
Thus, the answer is No, the card is not a face card.
Both statements together are sufficient to answer the question.
Therefore, the correct answer is (C) Both statements together are sufficient but neither statement alone is sufficient.
"The probability of drawing two Tens from the remaining 51 cards is
1/425
After drawing one card, there are 51 cards left in the deck. If the first card drawn is a Ten, there are 3 Tens left in the deck of 51 cards. The probability of drawing two Tens from the remaining 51 cards is:
P(Two Tens)=
Number of ways to choose 2 Tens from 3 / Number of ways to choose 2 cards from 51
= 3C2 / 51C2 = 3/(51×50/2) = 3/1275 = 1/425
This matches the given probability. Therefore, the first card drawn must have been a Ten.
Statement (2):
"The probability of drawing two Queens from the remaining 51 cards is
2/425
After drawing one card, there are 51 cards left in the deck. If the first card drawn is a Queen, there are 3 Queens left in the deck of 51 cards. The probability of drawing two Queens from the remaining 51 cards is:
P(Two Queens)= 3C2 / 51C2 = 3/1275 = 1/425
However, the given probability is
2/425
This suggests that the card drawn is not a Queen since drawing a Queen and then two Queens would not give this probability.
To get 2/425 , the calculation must consider a different scenario.
If the first card drawn was not a Queen but a different face card (King or Jack), then the probability of drawing two Queens from the remaining 51 cards would be different. Let's assume the card drawn was not a face card. If the card drawn was a non-face card, the probability of drawing two Queens would be:
P(Two Queens)= 4C2 / 51C2= 6/1275 = 2/425
This matches the given probability. Therefore, the card drawn is not a Queen, but a non-face card.
Conclusion:
Statement (1) alone tells us the card drawn is a Ten, which is not a face card.
Statement (2) alone tells us the card drawn is not a Queen, but it could be a non-face card.
Both statements together confirm that the card drawn is not a face card.
Thus, the answer is No, the card is not a face card.
Both statements together are sufficient to answer the question.
Therefore, the correct answer is (C) Both statements together are sufficient but neither statement alone is sufficient.
