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Two cards are drawn one by one at random without replacement from a pack of 52 cards. What is the probability that the cards drawn are queens?
- a)1/26
- b)2/13
- c)1/169
- d)1/221
Correct answer is option 'D'. Can you explain this answer?
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Two cards are drawn one by one at random without replacement from a pa...
Understanding the Problem
To find the probability that both cards drawn from a deck of 52 cards are queens, we need to consider the total number of ways to draw two cards and the favorable outcomes.
Total Outcomes
- The total number of ways to choose 2 cards from 52 is calculated using the combination formula:
- Total ways = C(52, 2) = 52! / (2!(52-2)!) = 52 * 51 / 2 = 1326.
Favorable Outcomes
- There are 4 queens in a standard deck of cards.
- The number of ways to choose 2 queens from the 4 available queens is:
- Favorable ways = C(4, 2) = 4! / (2!(4-2)!) = 4 * 3 / 2 = 6.
Calculating the Probability
- Now, the probability P that both cards drawn are queens is given by the ratio of the number of favorable outcomes to the total outcomes:
- P = (Number of favorable outcomes) / (Total outcomes)
- P = 6 / 1326 = 1 / 221.
Conclusion
- Therefore, the probability that both cards drawn are queens is:
- Option D: 1/221.
This calculation confirms that the correct answer is indeed option D.
To find the probability that both cards drawn from a deck of 52 cards are queens, we need to consider the total number of ways to draw two cards and the favorable outcomes.
Total Outcomes
- The total number of ways to choose 2 cards from 52 is calculated using the combination formula:
- Total ways = C(52, 2) = 52! / (2!(52-2)!) = 52 * 51 / 2 = 1326.
Favorable Outcomes
- There are 4 queens in a standard deck of cards.
- The number of ways to choose 2 queens from the 4 available queens is:
- Favorable ways = C(4, 2) = 4! / (2!(4-2)!) = 4 * 3 / 2 = 6.
Calculating the Probability
- Now, the probability P that both cards drawn are queens is given by the ratio of the number of favorable outcomes to the total outcomes:
- P = (Number of favorable outcomes) / (Total outcomes)
- P = 6 / 1326 = 1 / 221.
Conclusion
- Therefore, the probability that both cards drawn are queens is:
- Option D: 1/221.
This calculation confirms that the correct answer is indeed option D.
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Two cards are drawn one by one at random without replacement from a pack of 52 cards. What is the probability that the cards drawn are queens?a)1/26b)2/13c)1/169d)1/221Correct answer is option 'D'. Can you explain this answer?
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