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A box contains 11 cards with 1 to 11 consecutive numbers. If we take 5 cards in random without replacement from this box, what is the probability that the median of the numbers selected is 3?
- a)13/189
- b)11/128
- c)14/231
- d)None of the above
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A box contains 11 cards with 1 to 11 consecutive numbers. If we take 5...
The total number of ways of selecting 5 cards out of 11 is 11C5 
Now for favourable case, the third number should be 3. The first two numbers should be 1 and 2. The last two numbers can be selected out of the remaining 8 numbers in 8C2 = 28 ways.
Most Upvoted Answer
A box contains 11 cards with 1 to 11 consecutive numbers. If we take 5...
To find the probability that the median of the selected numbers is 3, we need to consider different cases where the number 3 can be the median.
There are a total of 11 cards numbered from 1 to 11.
Let's consider the different cases:
Case 1: 3 is the middle card
In this case, we can select 3 as the median card in 1 way. The remaining 4 cards can be selected from the remaining 10 cards in (10 choose 4) ways.
Case 2: 3 is the smallest card
In this case, we can select 3 as the smallest card in 1 way. The remaining 4 cards can be selected from the remaining 8 cards (excluding 1 and 2) in (8 choose 4) ways.
Case 3: 3 is the second smallest card
In this case, we can select 3 as the second smallest card in 1 way. The remaining 4 cards can be selected from the remaining 7 cards (excluding 1 and 2) in (7 choose 4) ways.
Case 4: 3 is the third smallest card
In this case, we can select 3 as the third smallest card in 1 way. The remaining 4 cards can be selected from the remaining 6 cards (excluding 1 and 2) in (6 choose 4) ways.
Case 5: 3 is the fourth smallest card
In this case, we can select 3 as the fourth smallest card in 1 way. The remaining 4 cards can be selected from the remaining 5 cards (excluding 1 and 2) in (5 choose 4) ways.
Case 6: 3 is the fifth smallest card
In this case, we can select 3 as the fifth smallest card in 1 way. The remaining 4 cards can be selected from the remaining 4 cards (excluding 1 and 2) in (4 choose 4) ways.
Total number of ways to select 5 cards from 11 cards without replacement = (11 choose 5)
Therefore, the probability that the median of the selected numbers is 3 is:
P(3 as the median) = (1 * (10 choose 4) + 1 * (8 choose 4) + 1 * (7 choose 4) + 1 * (6 choose 4) + 1 * (5 choose 4) + 1 * (4 choose 4)) / (11 choose 5)
Simplifying this expression:
P(3 as the median) = (10C4 + 8C4 + 7C4 + 6C4 + 5C4 + 4C4) / 11C5
Calculating the values:
P(3 as the median) = (210 + 70 + 35 + 15 + 5 + 1) / 462
P(3 as the median) = 336 / 462
P(3 as the median) = 14 / 231
Therefore, the correct answer is option C) 14/231.
There are a total of 11 cards numbered from 1 to 11.
Let's consider the different cases:
Case 1: 3 is the middle card
In this case, we can select 3 as the median card in 1 way. The remaining 4 cards can be selected from the remaining 10 cards in (10 choose 4) ways.
Case 2: 3 is the smallest card
In this case, we can select 3 as the smallest card in 1 way. The remaining 4 cards can be selected from the remaining 8 cards (excluding 1 and 2) in (8 choose 4) ways.
Case 3: 3 is the second smallest card
In this case, we can select 3 as the second smallest card in 1 way. The remaining 4 cards can be selected from the remaining 7 cards (excluding 1 and 2) in (7 choose 4) ways.
Case 4: 3 is the third smallest card
In this case, we can select 3 as the third smallest card in 1 way. The remaining 4 cards can be selected from the remaining 6 cards (excluding 1 and 2) in (6 choose 4) ways.
Case 5: 3 is the fourth smallest card
In this case, we can select 3 as the fourth smallest card in 1 way. The remaining 4 cards can be selected from the remaining 5 cards (excluding 1 and 2) in (5 choose 4) ways.
Case 6: 3 is the fifth smallest card
In this case, we can select 3 as the fifth smallest card in 1 way. The remaining 4 cards can be selected from the remaining 4 cards (excluding 1 and 2) in (4 choose 4) ways.
Total number of ways to select 5 cards from 11 cards without replacement = (11 choose 5)
Therefore, the probability that the median of the selected numbers is 3 is:
P(3 as the median) = (1 * (10 choose 4) + 1 * (8 choose 4) + 1 * (7 choose 4) + 1 * (6 choose 4) + 1 * (5 choose 4) + 1 * (4 choose 4)) / (11 choose 5)
Simplifying this expression:
P(3 as the median) = (10C4 + 8C4 + 7C4 + 6C4 + 5C4 + 4C4) / 11C5
Calculating the values:
P(3 as the median) = (210 + 70 + 35 + 15 + 5 + 1) / 462
P(3 as the median) = 336 / 462
P(3 as the median) = 14 / 231
Therefore, the correct answer is option C) 14/231.
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A box contains 11 cards with 1 to 11 consecutive numbers. If we take 5 cards in random without replacement from this box, what is the probability that the median of the numbers selected is 3?a)13/189b)11/128c)14/231d)None of the above Correct answer is option 'C'. Can you explain this answer?
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A box contains 11 cards with 1 to 11 consecutive numbers. If we take 5 cards in random without replacement from this box, what is the probability that the median of the numbers selected is 3?a)13/189b)11/128c)14/231d)None of the above Correct answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A box contains 11 cards with 1 to 11 consecutive numbers. If we take 5 cards in random without replacement from this box, what is the probability that the median of the numbers selected is 3?a)13/189b)11/128c)14/231d)None of the above Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A box contains 11 cards with 1 to 11 consecutive numbers. If we take 5 cards in random without replacement from this box, what is the probability that the median of the numbers selected is 3?a)13/189b)11/128c)14/231d)None of the above Correct answer is option 'C'. Can you explain this answer?.
A box contains 11 cards with 1 to 11 consecutive numbers. If we take 5 cards in random without replacement from this box, what is the probability that the median of the numbers selected is 3?a)13/189b)11/128c)14/231d)None of the above Correct answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A box contains 11 cards with 1 to 11 consecutive numbers. If we take 5 cards in random without replacement from this box, what is the probability that the median of the numbers selected is 3?a)13/189b)11/128c)14/231d)None of the above Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A box contains 11 cards with 1 to 11 consecutive numbers. If we take 5 cards in random without replacement from this box, what is the probability that the median of the numbers selected is 3?a)13/189b)11/128c)14/231d)None of the above Correct answer is option 'C'. Can you explain this answer?.
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A box contains 11 cards with 1 to 11 consecutive numbers. If we take 5 cards in random without replacement from this box, what is the probability that the median of the numbers selected is 3?a)13/189b)11/128c)14/231d)None of the above Correct answer is option 'C'. Can you explain this answer?, a detailed solution for A box contains 11 cards with 1 to 11 consecutive numbers. If we take 5 cards in random without replacement from this box, what is the probability that the median of the numbers selected is 3?a)13/189b)11/128c)14/231d)None of the above Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of A box contains 11 cards with 1 to 11 consecutive numbers. If we take 5 cards in random without replacement from this box, what is the probability that the median of the numbers selected is 3?a)13/189b)11/128c)14/231d)None of the above Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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