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A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be both diamonds. Find the Probability of the lost card being a diamond?
- a)12/50
- b)8/50
- c)11/50
- d)9/50
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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A card from a pack of 52 cards is lost. From the remaining cards of th...
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A card from a pack of 52 cards is lost. From the remaining cards of th...
Total cards = 52
Drawn cards(Heart) = 2
Present total cards = total cards-drawn cards =52-2=50
Remaining Card 13-2 = 11
Probability = 11/50
Drawn cards(Heart) = 2
Present total cards = total cards-drawn cards =52-2=50
Remaining Card 13-2 = 11
Probability = 11/50
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Community Answer
A card from a pack of 52 cards is lost. From the remaining cards of th...
To solve this problem, we need to use conditional probability. Let's break down the information given and use the formula for conditional probability:
P(A|B) = P(A ∩ B) / P(B)
where A and B are events.
Given:
- A card is lost from a pack of 52 cards.
- Two cards are drawn from the remaining cards and are both diamonds.
We need to find the probability of the lost card being a diamond.
Let's calculate the probabilities step by step:
Step 1: Find the probability of drawing two diamonds
The probability of drawing the first diamond is 13/52 since there are 13 diamonds in a deck of 52 cards.
After drawing the first diamond, there are 12 diamonds left in a deck of 51 cards.
So, the probability of drawing the second diamond, given that the first card was a diamond, is 12/51.
Using the multiplication rule, the probability of drawing two diamonds is (13/52) * (12/51).
Step 2: Find the probability of the lost card being a diamond
The lost card can be any of the remaining 50 cards. Since we know that two diamonds have already been drawn, there are 11 diamonds left in the remaining 50 cards.
So, the probability of the lost card being a diamond is 11/50.
Step 3: Apply the conditional probability formula
Using the formula for conditional probability, we have:
P(diamond|two diamonds) = P(diamond ∩ two diamonds) / P(two diamonds)
P(diamond ∩ two diamonds) is the probability of drawing two diamonds, which we calculated in Step 1.
P(two diamonds) is the probability of drawing two diamonds, which we calculated in Step 1.
Plugging in the values, we have:
P(diamond|two diamonds) = [(13/52) * (12/51)] / (13/52) * (12/51)
Simplifying the expression, we get:
P(diamond|two diamonds) = 11/50
Therefore, the probability of the lost card being a diamond is 11/50, which corresponds to option C.
P(A|B) = P(A ∩ B) / P(B)
where A and B are events.
Given:
- A card is lost from a pack of 52 cards.
- Two cards are drawn from the remaining cards and are both diamonds.
We need to find the probability of the lost card being a diamond.
Let's calculate the probabilities step by step:
Step 1: Find the probability of drawing two diamonds
The probability of drawing the first diamond is 13/52 since there are 13 diamonds in a deck of 52 cards.
After drawing the first diamond, there are 12 diamonds left in a deck of 51 cards.
So, the probability of drawing the second diamond, given that the first card was a diamond, is 12/51.
Using the multiplication rule, the probability of drawing two diamonds is (13/52) * (12/51).
Step 2: Find the probability of the lost card being a diamond
The lost card can be any of the remaining 50 cards. Since we know that two diamonds have already been drawn, there are 11 diamonds left in the remaining 50 cards.
So, the probability of the lost card being a diamond is 11/50.
Step 3: Apply the conditional probability formula
Using the formula for conditional probability, we have:
P(diamond|two diamonds) = P(diamond ∩ two diamonds) / P(two diamonds)
P(diamond ∩ two diamonds) is the probability of drawing two diamonds, which we calculated in Step 1.
P(two diamonds) is the probability of drawing two diamonds, which we calculated in Step 1.
Plugging in the values, we have:
P(diamond|two diamonds) = [(13/52) * (12/51)] / (13/52) * (12/51)
Simplifying the expression, we get:
P(diamond|two diamonds) = 11/50
Therefore, the probability of the lost card being a diamond is 11/50, which corresponds to option C.
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A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be both diamonds. Find the Probability of the lost card being a diamond?a)12/50b)8/50c)11/50d)9/50e)None of theseCorrect answer is option 'C'. Can you explain this answer?
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A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be both diamonds. Find the Probability of the lost card being a diamond?a)12/50b)8/50c)11/50d)9/50e)None of theseCorrect answer is option 'C'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be both diamonds. Find the Probability of the lost card being a diamond?a)12/50b)8/50c)11/50d)9/50e)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be both diamonds. Find the Probability of the lost card being a diamond?a)12/50b)8/50c)11/50d)9/50e)None of theseCorrect answer is option 'C'. Can you explain this answer?.
A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be both diamonds. Find the Probability of the lost card being a diamond?a)12/50b)8/50c)11/50d)9/50e)None of theseCorrect answer is option 'C'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be both diamonds. Find the Probability of the lost card being a diamond?a)12/50b)8/50c)11/50d)9/50e)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be both diamonds. Find the Probability of the lost card being a diamond?a)12/50b)8/50c)11/50d)9/50e)None of theseCorrect answer is option 'C'. Can you explain this answer?.
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