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A card is drawn from a pack of 52 cards. The card is drawn at random; find the probability that it is neither club nor queen?
- a)4/13
- b)5/13
- c)7/13
- d)9/13
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
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A card is drawn from a pack of 52 cards. The card is drawn at random; ...
1 – [13/52 + 4/52 – 1/52] = 9/13
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A card is drawn from a pack of 52 cards. The card is drawn at random; ...
To find the probability that a card drawn from a pack of 52 cards is neither a club nor a queen, we need to determine the number of favorable outcomes (cards that are neither a club nor a queen) and divide it by the total number of possible outcomes (all 52 cards).
Number of favorable outcomes:
- There are 13 clubs in a deck of cards, and there is only one queen of clubs. So, there are 13 - 1 = 12 cards that are clubs but not queens.
- There are 4 queens in a deck of cards, and one of them is the queen of clubs. So, there are 4 - 1 = 3 queens that are not clubs.
- Therefore, the number of cards that are neither a club nor a queen is 52 - (12 + 3) = 37.
Total number of possible outcomes:
- There are 52 cards in a deck.
So, the probability of drawing a card that is neither a club nor a queen is given by:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 37 / 52
Simplifying the fraction by dividing both the numerator and the denominator by 37, we get:
Probability = 1 / (52/37)
Probability = 1 / (4/3)
Probability = 1 * (3/4)
Probability = 3/4
Therefore, the probability that a card drawn from a pack of 52 cards is neither a club nor a queen is 3/4, which is equivalent to 9/13.
Hence, the correct answer is option D) 9/13.
Number of favorable outcomes:
- There are 13 clubs in a deck of cards, and there is only one queen of clubs. So, there are 13 - 1 = 12 cards that are clubs but not queens.
- There are 4 queens in a deck of cards, and one of them is the queen of clubs. So, there are 4 - 1 = 3 queens that are not clubs.
- Therefore, the number of cards that are neither a club nor a queen is 52 - (12 + 3) = 37.
Total number of possible outcomes:
- There are 52 cards in a deck.
So, the probability of drawing a card that is neither a club nor a queen is given by:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 37 / 52
Simplifying the fraction by dividing both the numerator and the denominator by 37, we get:
Probability = 1 / (52/37)
Probability = 1 / (4/3)
Probability = 1 * (3/4)
Probability = 3/4
Therefore, the probability that a card drawn from a pack of 52 cards is neither a club nor a queen is 3/4, which is equivalent to 9/13.
Hence, the correct answer is option D) 9/13.
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