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The probability that a card drawn at random from a pack of 52 cards is a king or a heart is
- a)16/52
- b)1/13
- c)1/52
- d)1/4
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
The probability that a card drawn at random from a pack of 52 cards is...
The number of kings in a deck are 4
Number of hearts in the deck are 13, including the king of hearts
Probability of getting either a king or a heart is, P = 4+(13–1) / 52
P = 16/52
Number of hearts in the deck are 13, including the king of hearts
Probability of getting either a king or a heart is, P = 4+(13–1) / 52
P = 16/52
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Community Answer
The probability that a card drawn at random from a pack of 52 cards is...
Given:
Total number of cards in a pack = 52
To find:
Probability of drawing a king or a heart
Solution:
There are 4 kings in a pack of cards (1 king of hearts, 1 king of diamonds, 1 king of clubs, and 1 king of spades).
There are 13 hearts in a pack of cards (including the king of hearts).
We need to find the probability of drawing a king or a heart. Let's calculate the number of favorable outcomes and the total number of possible outcomes.
Number of favorable outcomes:
There are 4 kings and 13 hearts in a pack of cards, but we need to subtract the king of hearts because it has already been counted as a king. So, the number of favorable outcomes is 4 + 13 - 1 = 16.
Total number of possible outcomes:
There are 52 cards in a pack, so the total number of possible outcomes is 52.
Probability:
Probability is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes.
Probability = Number of favorable outcomes / Total number of possible outcomes
Substituting the values, we get:
Probability = 16 / 52
Simplifying the fraction, we get:
Probability = 4 / 13
Therefore, the probability of drawing a king or a heart is 4/13, which is equivalent to option A (16/52).
Note: The probability can also be expressed as a decimal or percentage. In this case, 4/13 is approximately 0.3077 or 30.77%.
Total number of cards in a pack = 52
To find:
Probability of drawing a king or a heart
Solution:
There are 4 kings in a pack of cards (1 king of hearts, 1 king of diamonds, 1 king of clubs, and 1 king of spades).
There are 13 hearts in a pack of cards (including the king of hearts).
We need to find the probability of drawing a king or a heart. Let's calculate the number of favorable outcomes and the total number of possible outcomes.
Number of favorable outcomes:
There are 4 kings and 13 hearts in a pack of cards, but we need to subtract the king of hearts because it has already been counted as a king. So, the number of favorable outcomes is 4 + 13 - 1 = 16.
Total number of possible outcomes:
There are 52 cards in a pack, so the total number of possible outcomes is 52.
Probability:
Probability is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes.
Probability = Number of favorable outcomes / Total number of possible outcomes
Substituting the values, we get:
Probability = 16 / 52
Simplifying the fraction, we get:
Probability = 4 / 13
Therefore, the probability of drawing a king or a heart is 4/13, which is equivalent to option A (16/52).
Note: The probability can also be expressed as a decimal or percentage. In this case, 4/13 is approximately 0.3077 or 30.77%.
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