JEE Exam > JEE Questions > A student can solve 70% problems of a book an...
Start Learning for Free
A student can solve 70% problems of a book and second student solve 50% problem of same book. Find the probability that at least one of them will solve a selected problem from this book.
- a)13/20
- b)17/20
- c)3/20
- d)7/20
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A student can solve 70% problems of a book and second student solve 50...
Probability that first and second student can solve
=0.7×0.5=0.35
Probability that first can solve and second cannot solve
=0.7×0.5=0.35
Probability that first cannot solve and Amisha can solve
=0.3×0.5=0.15
Therefore, probability that at least one of them will solve
=0.35+0.35+0.15 = 0.85
=> 85/100
= 17/20
=0.7×0.5=0.35
Probability that first can solve and second cannot solve
=0.7×0.5=0.35
Probability that first cannot solve and Amisha can solve
=0.3×0.5=0.15
Therefore, probability that at least one of them will solve
=0.35+0.35+0.15 = 0.85
=> 85/100
= 17/20
Free Test
FREE
| Start Free Test |
Community Answer
A student can solve 70% problems of a book and second student solve 50...
Solution:
Given, the first student solves 70% of the problems and the second student solves 50% of the problems.
Let A be the event that the first student solves a selected problem and B be the event that the second student solves a selected problem.
Then, the probability that at least one of them will solve a selected problem is given by P(A ∪ B).
Using the formula for the union of two events, we have
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
where P(A) is the probability that the first student solves a selected problem, P(B) is the probability that the second student solves a selected problem, and P(A ∩ B) is the probability that both of them solve a selected problem.
We know that P(A) = 0.7 and P(B) = 0.5.
To find P(A ∩ B), we note that both students can solve a selected problem only if the selected problem is solved by both of them. Therefore, P(A ∩ B) = P(A) × P(B) = 0.7 × 0.5 = 0.35.
Substituting these values in the formula, we get
P(A ∪ B) = 0.7 + 0.5 - 0.35 = 0.85
Therefore, the probability that at least one of them will solve a selected problem is 0.85 or 17/20.
Hence, the correct answer is option (B).
Given, the first student solves 70% of the problems and the second student solves 50% of the problems.
Let A be the event that the first student solves a selected problem and B be the event that the second student solves a selected problem.
Then, the probability that at least one of them will solve a selected problem is given by P(A ∪ B).
Using the formula for the union of two events, we have
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
where P(A) is the probability that the first student solves a selected problem, P(B) is the probability that the second student solves a selected problem, and P(A ∩ B) is the probability that both of them solve a selected problem.
We know that P(A) = 0.7 and P(B) = 0.5.
To find P(A ∩ B), we note that both students can solve a selected problem only if the selected problem is solved by both of them. Therefore, P(A ∩ B) = P(A) × P(B) = 0.7 × 0.5 = 0.35.
Substituting these values in the formula, we get
P(A ∪ B) = 0.7 + 0.5 - 0.35 = 0.85
Therefore, the probability that at least one of them will solve a selected problem is 0.85 or 17/20.
Hence, the correct answer is option (B).
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
A student can solve 70% problems of a book and second student solve 50% problem of same book. Find the probability that at least one of them will solve a selected problem from this book.a)13/20b)17/20c)3/20d)7/20Correct answer is option 'B'. Can you explain this answer?
Question Description
A student can solve 70% problems of a book and second student solve 50% problem of same book. Find the probability that at least one of them will solve a selected problem from this book.a)13/20b)17/20c)3/20d)7/20Correct answer is option 'B'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A student can solve 70% problems of a book and second student solve 50% problem of same book. Find the probability that at least one of them will solve a selected problem from this book.a)13/20b)17/20c)3/20d)7/20Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A student can solve 70% problems of a book and second student solve 50% problem of same book. Find the probability that at least one of them will solve a selected problem from this book.a)13/20b)17/20c)3/20d)7/20Correct answer is option 'B'. Can you explain this answer?.
A student can solve 70% problems of a book and second student solve 50% problem of same book. Find the probability that at least one of them will solve a selected problem from this book.a)13/20b)17/20c)3/20d)7/20Correct answer is option 'B'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A student can solve 70% problems of a book and second student solve 50% problem of same book. Find the probability that at least one of them will solve a selected problem from this book.a)13/20b)17/20c)3/20d)7/20Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A student can solve 70% problems of a book and second student solve 50% problem of same book. Find the probability that at least one of them will solve a selected problem from this book.a)13/20b)17/20c)3/20d)7/20Correct answer is option 'B'. Can you explain this answer?.
Solutions for A student can solve 70% problems of a book and second student solve 50% problem of same book. Find the probability that at least one of them will solve a selected problem from this book.a)13/20b)17/20c)3/20d)7/20Correct answer is option 'B'. 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 A student can solve 70% problems of a book and second student solve 50% problem of same book. Find the probability that at least one of them will solve a selected problem from this book.a)13/20b)17/20c)3/20d)7/20Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A student can solve 70% problems of a book and second student solve 50% problem of same book. Find the probability that at least one of them will solve a selected problem from this book.a)13/20b)17/20c)3/20d)7/20Correct answer is option 'B'. Can you explain this answer?, a detailed solution for A student can solve 70% problems of a book and second student solve 50% problem of same book. Find the probability that at least one of them will solve a selected problem from this book.a)13/20b)17/20c)3/20d)7/20Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of A student can solve 70% problems of a book and second student solve 50% problem of same book. Find the probability that at least one of them will solve a selected problem from this book.a)13/20b)17/20c)3/20d)7/20Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A student can solve 70% problems of a book and second student solve 50% problem of same book. Find the probability that at least one of them will solve a selected problem from this book.a)13/20b)17/20c)3/20d)7/20Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
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