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From a pack of 52 cards, two are drawn at random. Find the chance that one is a knave and the other a queen.
- a)8/663
- b)1/6
- c)1/9
- d)1/12
Correct answer is option 'A'. Can you explain this answer?
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From a pack of 52 cards, two are drawn at random. Find the chance that...
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From a pack of 52 cards, two are drawn at random. Find the chance that...
To find the chance that one card drawn is a knave (jack) and the other is a queen, we need to determine the number of favorable outcomes and the total number of possible outcomes.
Number of favorable outcomes:
There are 4 knaves and 4 queens in a deck of 52 cards. Since we need one knave and one queen, we can choose any one of the 4 knaves and any one of the 4 queens. Therefore, the number of favorable outcomes is 4 * 4 = 16.
Total number of possible outcomes:
When two cards are drawn from a deck of 52 cards, the total number of possible outcomes can be calculated using the concept of combinations. We can choose any 2 cards out of the 52 cards in the deck. Therefore, the total number of possible outcomes is given by the combination formula C(52, 2) = (52!)/(2!(52-2)!) = 1326.
Calculating the chance (probability):
The probability of an event happening is given by the formula:
Probability = (Number of favorable outcomes)/(Total number of possible outcomes).
Plugging in the values:
Probability = 16/1326
Simplifying the fraction:
Probability = 8/663
Therefore, the chance that one card drawn is a knave and the other is a queen is 8/663.
Hence, option A) 8/663 is the correct answer.
Number of favorable outcomes:
There are 4 knaves and 4 queens in a deck of 52 cards. Since we need one knave and one queen, we can choose any one of the 4 knaves and any one of the 4 queens. Therefore, the number of favorable outcomes is 4 * 4 = 16.
Total number of possible outcomes:
When two cards are drawn from a deck of 52 cards, the total number of possible outcomes can be calculated using the concept of combinations. We can choose any 2 cards out of the 52 cards in the deck. Therefore, the total number of possible outcomes is given by the combination formula C(52, 2) = (52!)/(2!(52-2)!) = 1326.
Calculating the chance (probability):
The probability of an event happening is given by the formula:
Probability = (Number of favorable outcomes)/(Total number of possible outcomes).
Plugging in the values:
Probability = 16/1326
Simplifying the fraction:
Probability = 8/663
Therefore, the chance that one card drawn is a knave and the other is a queen is 8/663.
Hence, option A) 8/663 is the correct answer.
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From a pack of 52 cards, two are drawn at random. Find the chance that one is a knave and the other a queen.a)8/663b)1/6c)1/9d)1/12Correct answer is option 'A'. Can you explain this answer?
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