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A card is drawn from a pack of playing cards and then another card is drawn without the first being replaced. What is the probability of getting two hearts?
- a)1/17
- b)1/4
- c)2/17
- d)None of these.
Correct answer is option 'A'. Can you explain this answer?
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A card is drawn from a pack of playing cards and then another card is ...
Probability of Getting Two Hearts from a Pack of Playing Cards
Given: A card is drawn from a pack of playing cards and then another card is drawn without the first being replaced.
To find: The probability of getting two hearts.
Solution:
Total number of cards in a pack of playing cards = 52.
Total number of hearts in a pack of playing cards = 13.
1. Probability of getting a heart in the first draw = 13/52 = 1/4.
2. After the first card is drawn, the total number of cards in the pack reduces to 51.
Total number of hearts in the pack remains the same, i.e., 13.
Probability of getting a heart in the second draw, without replacement = 12/51.
[Since one heart has already been drawn and not replaced, the total number of cards in the pack has reduced to 51 and the total number of hearts has reduced to 12.]
3. Probability of getting two hearts = Probability of getting a heart in the first draw × Probability of getting a heart in the second draw, without replacement.
= (13/52) × (12/51)
= (13 × 12)/(52 × 51)
= 1/17
Therefore, the probability of getting two hearts from a pack of playing cards is 1/17.
Answer: Option (a) 1/17.
Given: A card is drawn from a pack of playing cards and then another card is drawn without the first being replaced.
To find: The probability of getting two hearts.
Solution:
Total number of cards in a pack of playing cards = 52.
Total number of hearts in a pack of playing cards = 13.
1. Probability of getting a heart in the first draw = 13/52 = 1/4.
2. After the first card is drawn, the total number of cards in the pack reduces to 51.
Total number of hearts in the pack remains the same, i.e., 13.
Probability of getting a heart in the second draw, without replacement = 12/51.
[Since one heart has already been drawn and not replaced, the total number of cards in the pack has reduced to 51 and the total number of hearts has reduced to 12.]
3. Probability of getting two hearts = Probability of getting a heart in the first draw × Probability of getting a heart in the second draw, without replacement.
= (13/52) × (12/51)
= (13 × 12)/(52 × 51)
= 1/17
Therefore, the probability of getting two hearts from a pack of playing cards is 1/17.
Answer: Option (a) 1/17.
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Community Answer
A card is drawn from a pack of playing cards and then another card is ...
13/52 *12/51=
156/2652=1/17
156/2652=1/17
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