CLAT Exam > CLAT Questions > DIRECTIONS for the question: Solve the follo...
Start Learning for Free
DIRECTIONS for the question: Solve the following question and mark the best possible option.
P, Q and R are positive integers such that P+Q+R=100. Find the probability that P >20, Q > 10 and R>20.?
- a)23/99
- b)8/33
- c)2/9
- d)⅓
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
DIRECTIONS for the question: Solve the following question and mark th...
P+Q+R=100
View all questions of this test
Total number of natural number solutions.
(100-1)C(3-1) = (99x 98)/2
Let P=a+20, Q=b+10,z=c+20. where a, b , c are natural numbers.
∴ Substituting we get a+b+c=50
The number of natural number solutions for this equation is (50 - 1)C(3-1)
= 49C2 = (49x48)/2
∴ Required probability = (49 x 24)/(49 x 99) = 24/99 = 8/33
Most Upvoted Answer
DIRECTIONS for the question: Solve the following question and mark th...
Calculation for Probability:
The total number of ways in which the positive integers P, Q, and R can sum up to 100 is determined by the number of solutions to the equation P + Q + R = 100.
This is a classic stars and bars problem, and the number of ways to distribute 100 identical stars into 3 distinct boxes is given by C(100+3-1, 3-1) = C(102, 2).
Finding the Favorable Cases:
To find the probability that P > 20, Q > 10, and R > 20, we first calculate the number of ways in which P, Q, and R can be distributed when each of them satisfies the given conditions.
Let's say P' = P - 21, Q' = Q - 11, and R' = R - 21. Therefore, P' + Q' + R' = 100 - 21 - 11 - 21 = 47.
The number of solutions to this equation is C(47+3-1, 3-1) = C(49, 2).
Calculating Probability:
The probability of P > 20, Q > 10, and R > 20 is given by the ratio of the number of favorable cases to the total number of cases:
Probability = C(49, 2)/C(102, 2) = 1148/5151 = 8/33.
Therefore, the correct answer is option 'b) 8/33'.
The total number of ways in which the positive integers P, Q, and R can sum up to 100 is determined by the number of solutions to the equation P + Q + R = 100.
This is a classic stars and bars problem, and the number of ways to distribute 100 identical stars into 3 distinct boxes is given by C(100+3-1, 3-1) = C(102, 2).
Finding the Favorable Cases:
To find the probability that P > 20, Q > 10, and R > 20, we first calculate the number of ways in which P, Q, and R can be distributed when each of them satisfies the given conditions.
Let's say P' = P - 21, Q' = Q - 11, and R' = R - 21. Therefore, P' + Q' + R' = 100 - 21 - 11 - 21 = 47.
The number of solutions to this equation is C(47+3-1, 3-1) = C(49, 2).
Calculating Probability:
The probability of P > 20, Q > 10, and R > 20 is given by the ratio of the number of favorable cases to the total number of cases:
Probability = C(49, 2)/C(102, 2) = 1148/5151 = 8/33.
Therefore, the correct answer is option 'b) 8/33'.
Attention CLAT Students!
To make sure you are not studying endlessly, EduRev has designed CLAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CLAT.
|
Explore Courses for CLAT exam
|
|
Similar CLAT Doubts
Top Courses for CLATView all
DIRECTIONS for the question: Solve the following question and mark the best possible option.P, Q and R are positive integers such that P+Q+R=100. Find the probability that P >20, Q > 10 and R>20.?a)23/99b)8/33c)2/9d)⅓Correct answer is option 'B'. Can you explain this answer?
Question Description
DIRECTIONS for the question: Solve the following question and mark the best possible option.P, Q and R are positive integers such that P+Q+R=100. Find the probability that P >20, Q > 10 and R>20.?a)23/99b)8/33c)2/9d)⅓Correct answer is option 'B'. Can you explain this answer? for CLAT 2024 is part of CLAT preparation. The Question and answers have been prepared according to the CLAT exam syllabus. Information about DIRECTIONS for the question: Solve the following question and mark the best possible option.P, Q and R are positive integers such that P+Q+R=100. Find the probability that P >20, Q > 10 and R>20.?a)23/99b)8/33c)2/9d)⅓Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CLAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for DIRECTIONS for the question: Solve the following question and mark the best possible option.P, Q and R are positive integers such that P+Q+R=100. Find the probability that P >20, Q > 10 and R>20.?a)23/99b)8/33c)2/9d)⅓Correct answer is option 'B'. Can you explain this answer?.
DIRECTIONS for the question: Solve the following question and mark the best possible option.P, Q and R are positive integers such that P+Q+R=100. Find the probability that P >20, Q > 10 and R>20.?a)23/99b)8/33c)2/9d)⅓Correct answer is option 'B'. Can you explain this answer? for CLAT 2024 is part of CLAT preparation. The Question and answers have been prepared according to the CLAT exam syllabus. Information about DIRECTIONS for the question: Solve the following question and mark the best possible option.P, Q and R are positive integers such that P+Q+R=100. Find the probability that P >20, Q > 10 and R>20.?a)23/99b)8/33c)2/9d)⅓Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CLAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for DIRECTIONS for the question: Solve the following question and mark the best possible option.P, Q and R are positive integers such that P+Q+R=100. Find the probability that P >20, Q > 10 and R>20.?a)23/99b)8/33c)2/9d)⅓Correct answer is option 'B'. Can you explain this answer?.
Solutions for DIRECTIONS for the question: Solve the following question and mark the best possible option.P, Q and R are positive integers such that P+Q+R=100. Find the probability that P >20, Q > 10 and R>20.?a)23/99b)8/33c)2/9d)⅓Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for CLAT.
Download more important topics, notes, lectures and mock test series for CLAT Exam by signing up for free.
Here you can find the meaning of DIRECTIONS for the question: Solve the following question and mark the best possible option.P, Q and R are positive integers such that P+Q+R=100. Find the probability that P >20, Q > 10 and R>20.?a)23/99b)8/33c)2/9d)⅓Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
DIRECTIONS for the question: Solve the following question and mark the best possible option.P, Q and R are positive integers such that P+Q+R=100. Find the probability that P >20, Q > 10 and R>20.?a)23/99b)8/33c)2/9d)⅓Correct answer is option 'B'. Can you explain this answer?, a detailed solution for DIRECTIONS for the question: Solve the following question and mark the best possible option.P, Q and R are positive integers such that P+Q+R=100. Find the probability that P >20, Q > 10 and R>20.?a)23/99b)8/33c)2/9d)⅓Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of DIRECTIONS for the question: Solve the following question and mark the best possible option.P, Q and R are positive integers such that P+Q+R=100. Find the probability that P >20, Q > 10 and R>20.?a)23/99b)8/33c)2/9d)⅓Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice DIRECTIONS for the question: Solve the following question and mark the best possible option.P, Q and R are positive integers such that P+Q+R=100. Find the probability that P >20, Q > 10 and R>20.?a)23/99b)8/33c)2/9d)⅓Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice CLAT tests.
|
|
Explore Courses for CLAT 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
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup