Quant Exam > Quant Questions > Three numbers are chosen at random without re...
Start Learning for Free
Three numbers are chosen at random without replacement from (1, 2, 3 ..., 10). The probability that the minimum number is 3 or the maximum number is 7 is
- a)12/37
- b)11/40
- c)13/35
- d)14/35
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Three numbers are chosen at random without replacement from (1, 2, 3 ....
Most Upvoted Answer
Three numbers are chosen at random without replacement from (1, 2, 3 ....
Given information:
Three numbers are chosen at random without replacement from (1, 2, 3 ..., 10).
To find:
The probability that the minimum number is 3 or the maximum number is 7.
Solution:
Step 1:
Total number of outcomes:
When three numbers are chosen from (1, 2, 3 ..., 10) without replacement, the total number of outcomes is given by the combination formula:
nCr = n! / (r!(n-r)!)
Here, n = 10 (total numbers to choose from)
r = 3 (number of numbers chosen)
Total number of outcomes = 10C3 = 10! / (3!(10-3)!) = 10! / (3!7!) = (10*9*8*7!)/(3*2*1*7!) = (10*9*8)/(3*2*1) = 120
Hence, there are 120 possible outcomes.
Step 2:
Favorable outcomes:
To find the favorable outcomes, we need to consider two cases separately:
Case 1: The minimum number is 3
Case 2: The maximum number is 7
Case 1: The minimum number is 3
If the minimum number is 3, then we can choose the other two numbers from the remaining 9 numbers (4, 5, 6, 7, 8, 9, 10). The number of ways to choose 2 numbers from 9 is given by the combination formula:
9C2 = 9! / (2!(9-2)!) = 9! / (2!7!) = (9*8)/(2*1) = 36
Case 2: The maximum number is 7
If the maximum number is 7, then we can choose the other two numbers from the remaining 9 numbers (1, 2, 3, 4, 5, 6). The number of ways to choose 2 numbers from 6 is given by the combination formula:
6C2 = 6! / (2!(6-2)!) = 6! / (2!4!) = (6*5)/(2*1) = 15
Total favorable outcomes:
Total favorable outcomes = favorable outcomes in Case 1 + favorable outcomes in Case 2 = 36 + 15 = 51
Step 3:
Probability:
Probability = (Total favorable outcomes) / (Total number of outcomes) = 51 / 120 = 17 / 40
Therefore, the probability that the minimum number is 3 or the maximum number is 7 is 17/40, which is equivalent to option B.
Three numbers are chosen at random without replacement from (1, 2, 3 ..., 10).
To find:
The probability that the minimum number is 3 or the maximum number is 7.
Solution:
Step 1:
Total number of outcomes:
When three numbers are chosen from (1, 2, 3 ..., 10) without replacement, the total number of outcomes is given by the combination formula:
nCr = n! / (r!(n-r)!)
Here, n = 10 (total numbers to choose from)
r = 3 (number of numbers chosen)
Total number of outcomes = 10C3 = 10! / (3!(10-3)!) = 10! / (3!7!) = (10*9*8*7!)/(3*2*1*7!) = (10*9*8)/(3*2*1) = 120
Hence, there are 120 possible outcomes.
Step 2:
Favorable outcomes:
To find the favorable outcomes, we need to consider two cases separately:
Case 1: The minimum number is 3
Case 2: The maximum number is 7
Case 1: The minimum number is 3
If the minimum number is 3, then we can choose the other two numbers from the remaining 9 numbers (4, 5, 6, 7, 8, 9, 10). The number of ways to choose 2 numbers from 9 is given by the combination formula:
9C2 = 9! / (2!(9-2)!) = 9! / (2!7!) = (9*8)/(2*1) = 36
Case 2: The maximum number is 7
If the maximum number is 7, then we can choose the other two numbers from the remaining 9 numbers (1, 2, 3, 4, 5, 6). The number of ways to choose 2 numbers from 6 is given by the combination formula:
6C2 = 6! / (2!(6-2)!) = 6! / (2!4!) = (6*5)/(2*1) = 15
Total favorable outcomes:
Total favorable outcomes = favorable outcomes in Case 1 + favorable outcomes in Case 2 = 36 + 15 = 51
Step 3:
Probability:
Probability = (Total favorable outcomes) / (Total number of outcomes) = 51 / 120 = 17 / 40
Therefore, the probability that the minimum number is 3 or the maximum number is 7 is 17/40, which is equivalent to option B.
Free Test
FREE
| Start Free Test |
Community Answer
Three numbers are chosen at random without replacement from (1, 2, 3 ....
Sample space =10C3 =120,
no. of ways to select 3 as minimum=7C2=21
no. of ways to select 7 as maximum=6C2=15
But 4,5,6 are being repeated in 2 cases, so favourable ways are 7C2+6C2-3C2=33
req probability=33/120=11/40
no. of ways to select 3 as minimum=7C2=21
no. of ways to select 7 as maximum=6C2=15
But 4,5,6 are being repeated in 2 cases, so favourable ways are 7C2+6C2-3C2=33
req probability=33/120=11/40
|
Explore Courses for Quant exam
|
|
Similar Quant Doubts
Three numbers are chosen at random without replacement from (1, 2, 3 ..., 10). The probability that the minimum number is 3 or the maximum number is 7 isa)12/37b)11/40c)13/35d)14/35Correct answer is option 'B'. Can you explain this answer?
Question Description
Three numbers are chosen at random without replacement from (1, 2, 3 ..., 10). The probability that the minimum number is 3 or the maximum number is 7 isa)12/37b)11/40c)13/35d)14/35Correct answer is option 'B'. 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 Three numbers are chosen at random without replacement from (1, 2, 3 ..., 10). The probability that the minimum number is 3 or the maximum number is 7 isa)12/37b)11/40c)13/35d)14/35Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three numbers are chosen at random without replacement from (1, 2, 3 ..., 10). The probability that the minimum number is 3 or the maximum number is 7 isa)12/37b)11/40c)13/35d)14/35Correct answer is option 'B'. Can you explain this answer?.
Three numbers are chosen at random without replacement from (1, 2, 3 ..., 10). The probability that the minimum number is 3 or the maximum number is 7 isa)12/37b)11/40c)13/35d)14/35Correct answer is option 'B'. 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 Three numbers are chosen at random without replacement from (1, 2, 3 ..., 10). The probability that the minimum number is 3 or the maximum number is 7 isa)12/37b)11/40c)13/35d)14/35Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three numbers are chosen at random without replacement from (1, 2, 3 ..., 10). The probability that the minimum number is 3 or the maximum number is 7 isa)12/37b)11/40c)13/35d)14/35Correct answer is option 'B'. Can you explain this answer?.
Solutions for Three numbers are chosen at random without replacement from (1, 2, 3 ..., 10). The probability that the minimum number is 3 or the maximum number is 7 isa)12/37b)11/40c)13/35d)14/35Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Quant.
Download more important topics, notes, lectures and mock test series for Quant Exam by signing up for free.
Here you can find the meaning of Three numbers are chosen at random without replacement from (1, 2, 3 ..., 10). The probability that the minimum number is 3 or the maximum number is 7 isa)12/37b)11/40c)13/35d)14/35Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Three numbers are chosen at random without replacement from (1, 2, 3 ..., 10). The probability that the minimum number is 3 or the maximum number is 7 isa)12/37b)11/40c)13/35d)14/35Correct answer is option 'B'. Can you explain this answer?, a detailed solution for Three numbers are chosen at random without replacement from (1, 2, 3 ..., 10). The probability that the minimum number is 3 or the maximum number is 7 isa)12/37b)11/40c)13/35d)14/35Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of Three numbers are chosen at random without replacement from (1, 2, 3 ..., 10). The probability that the minimum number is 3 or the maximum number is 7 isa)12/37b)11/40c)13/35d)14/35Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Three numbers are chosen at random without replacement from (1, 2, 3 ..., 10). The probability that the minimum number is 3 or the maximum number is 7 isa)12/37b)11/40c)13/35d)14/35Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice Quant tests.
|
|
Explore Courses for Quant exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup