JEE Exam > JEE Questions > The probabilities of solving a problem by thr...
Start Learning for Free
The probabilities of solving a problem by three student A,B,C are 1/2, 1/3, 1/4 respectively. The probability that problem will be solved is
- a)1/4
- b)1/2
- c)3/4
- d)1/3
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
The probabilities of solving a problem by three student A,B,C are 1/2,...
We have, probability that A can solve the problem = P(A) = 1/2 ,
And in this way P(B) = 1/3 and P(C) = 1/4.
P(A cannot solve the problem) = 1 – P(A) = 1/2 ,
P(B cannot solve the problem) = 1 – P(B) = 1 – 1/3 = 2/3,
P(C cannot solve the problem) = 1 – P(C) = 1 – 1/4 = 3/4.
P(A, B, and C cannot solve the problem) = 1/2 x 2/3 x 3/4 = 1/4.
Therefore , P(Problem will be solve) = 1 – P(Problem is not solved by any of them)
= 1 – 1/4 = 3/4
And in this way P(B) = 1/3 and P(C) = 1/4.
P(A cannot solve the problem) = 1 – P(A) = 1/2 ,
P(B cannot solve the problem) = 1 – P(B) = 1 – 1/3 = 2/3,
P(C cannot solve the problem) = 1 – P(C) = 1 – 1/4 = 3/4.
P(A, B, and C cannot solve the problem) = 1/2 x 2/3 x 3/4 = 1/4.
Therefore , P(Problem will be solve) = 1 – P(Problem is not solved by any of them)
= 1 – 1/4 = 3/4
Most Upvoted Answer
The probabilities of solving a problem by three student A,B,C are 1/2,...
Problem Statement:
The probabilities of solving a problem by three students A, B, C are 1/2, 1/3, 1/4 respectively. The probability that the problem will be solved is:
Solution:
To find the probability that the problem will be solved, we need to find the probability that at least one of the students solves the problem.
Probability of A solving the problem:
The probability of A solving the problem is given as 1/2.
Probability of B solving the problem:
The probability of B solving the problem is given as 1/3.
Probability of C solving the problem:
The probability of C solving the problem is given as 1/4.
Probability that at least one of the students solves the problem:
To find the probability that at least one of the students solves the problem, we can use the complementary probability.
The complementary probability is the probability that the event does not occur. In this case, the event is that none of the students solve the problem.
The probability that none of the students solve the problem is the product of the probabilities that each student does not solve the problem.
The probability that A does not solve the problem is 1 - (1/2) = 1/2.
The probability that B does not solve the problem is 1 - (1/3) = 2/3.
The probability that C does not solve the problem is 1 - (1/4) = 3/4.
The probability that none of the students solve the problem is (1/2) * (2/3) * (3/4) = 1/4.
Therefore, the probability that at least one of the students solves the problem is 1 - (1/4) = 3/4.
Hence, the correct answer is option C) 3/4.
The probabilities of solving a problem by three students A, B, C are 1/2, 1/3, 1/4 respectively. The probability that the problem will be solved is:
Solution:
To find the probability that the problem will be solved, we need to find the probability that at least one of the students solves the problem.
Probability of A solving the problem:
The probability of A solving the problem is given as 1/2.
Probability of B solving the problem:
The probability of B solving the problem is given as 1/3.
Probability of C solving the problem:
The probability of C solving the problem is given as 1/4.
Probability that at least one of the students solves the problem:
To find the probability that at least one of the students solves the problem, we can use the complementary probability.
The complementary probability is the probability that the event does not occur. In this case, the event is that none of the students solve the problem.
The probability that none of the students solve the problem is the product of the probabilities that each student does not solve the problem.
The probability that A does not solve the problem is 1 - (1/2) = 1/2.
The probability that B does not solve the problem is 1 - (1/3) = 2/3.
The probability that C does not solve the problem is 1 - (1/4) = 3/4.
The probability that none of the students solve the problem is (1/2) * (2/3) * (3/4) = 1/4.
Therefore, the probability that at least one of the students solves the problem is 1 - (1/4) = 3/4.
Hence, the correct answer is option C) 3/4.
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Top Courses for JEEView all
The probabilities of solving a problem by three student A,B,C are 1/2, 1/3, 1/4 respectively. The probability that problem will be solved isa)1/4b)1/2c)3/4d)1/3Correct answer is option 'C'. Can you explain this answer?
Question Description
The probabilities of solving a problem by three student A,B,C are 1/2, 1/3, 1/4 respectively. The probability that problem will be solved isa)1/4b)1/2c)3/4d)1/3Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The probabilities of solving a problem by three student A,B,C are 1/2, 1/3, 1/4 respectively. The probability that problem will be solved isa)1/4b)1/2c)3/4d)1/3Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The probabilities of solving a problem by three student A,B,C are 1/2, 1/3, 1/4 respectively. The probability that problem will be solved isa)1/4b)1/2c)3/4d)1/3Correct answer is option 'C'. Can you explain this answer?.
The probabilities of solving a problem by three student A,B,C are 1/2, 1/3, 1/4 respectively. The probability that problem will be solved isa)1/4b)1/2c)3/4d)1/3Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The probabilities of solving a problem by three student A,B,C are 1/2, 1/3, 1/4 respectively. The probability that problem will be solved isa)1/4b)1/2c)3/4d)1/3Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The probabilities of solving a problem by three student A,B,C are 1/2, 1/3, 1/4 respectively. The probability that problem will be solved isa)1/4b)1/2c)3/4d)1/3Correct answer is option 'C'. Can you explain this answer?.
Solutions for The probabilities of solving a problem by three student A,B,C are 1/2, 1/3, 1/4 respectively. The probability that problem will be solved isa)1/4b)1/2c)3/4d)1/3Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of The probabilities of solving a problem by three student A,B,C are 1/2, 1/3, 1/4 respectively. The probability that problem will be solved isa)1/4b)1/2c)3/4d)1/3Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The probabilities of solving a problem by three student A,B,C are 1/2, 1/3, 1/4 respectively. The probability that problem will be solved isa)1/4b)1/2c)3/4d)1/3Correct answer is option 'C'. Can you explain this answer?, a detailed solution for The probabilities of solving a problem by three student A,B,C are 1/2, 1/3, 1/4 respectively. The probability that problem will be solved isa)1/4b)1/2c)3/4d)1/3Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of The probabilities of solving a problem by three student A,B,C are 1/2, 1/3, 1/4 respectively. The probability that problem will be solved isa)1/4b)1/2c)3/4d)1/3Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The probabilities of solving a problem by three student A,B,C are 1/2, 1/3, 1/4 respectively. The probability that problem will be solved isa)1/4b)1/2c)3/4d)1/3Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE 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