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Consider a pack of 52 cards. One card is drawn at random. What is the probability of the card being a heart or a seven?
- a)1/52
- b)4/13
- c)1/26
- d)17/52
Correct answer is option 'B'. Can you explain this answer?
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Consider a pack of 52 cards. One card is drawn at random. What is the ...
Probability of drawing a heart or a seven from a pack of 52 cards:
There are 52 cards in a standard deck of playing cards, and each card belongs to one of four suits - hearts, diamonds, clubs, or spades. Each suit contains 13 cards, including an ace, numbers 2 through 10, and three face cards (jack, queen, and king).
We are interested in finding the probability of drawing a card that is either a heart or a seven.
Total number of hearts:
There are 13 hearts in a deck of cards, so the probability of drawing a heart is 13/52.
Total number of sevens:
There are four sevens in a deck of cards (7 of hearts, 7 of diamonds, 7 of clubs, and 7 of spades), so the probability of drawing a seven is 4/52.
However, we need to be careful not to count the 7 of hearts twice, as it is both a heart and a seven. So, to find the probability of drawing a heart or a seven, we need to subtract the probability of drawing the 7 of hearts twice.
Probability of drawing the 7 of hearts:
There is only one 7 of hearts in the deck, so the probability of drawing it is 1/52.
Therefore, the probability of drawing a heart or a seven is:
(13/52) + (4/52) - (1/52) = 16/52 = 4/13.
Hence, the correct answer is option 'B' - 4/13.
There are 52 cards in a standard deck of playing cards, and each card belongs to one of four suits - hearts, diamonds, clubs, or spades. Each suit contains 13 cards, including an ace, numbers 2 through 10, and three face cards (jack, queen, and king).
We are interested in finding the probability of drawing a card that is either a heart or a seven.
Total number of hearts:
There are 13 hearts in a deck of cards, so the probability of drawing a heart is 13/52.
Total number of sevens:
There are four sevens in a deck of cards (7 of hearts, 7 of diamonds, 7 of clubs, and 7 of spades), so the probability of drawing a seven is 4/52.
However, we need to be careful not to count the 7 of hearts twice, as it is both a heart and a seven. So, to find the probability of drawing a heart or a seven, we need to subtract the probability of drawing the 7 of hearts twice.
Probability of drawing the 7 of hearts:
There is only one 7 of hearts in the deck, so the probability of drawing it is 1/52.
Therefore, the probability of drawing a heart or a seven is:
(13/52) + (4/52) - (1/52) = 16/52 = 4/13.
Hence, the correct answer is option 'B' - 4/13.
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Consider a pack of 52 cards. One card is drawn at random. What is the probability of the card being a heart or a seven?a)1/52b)4/13c)1/26d)17/52Correct answer is option 'B'. Can you explain this answer?
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