JEE Exam > JEE Questions > Box A contains 2 black and 3 red balls, while...
Start Learning for Free
Box A contains 2 black and 3 red balls, while box B contains 3 black and 4 red balls. Out of these two boxes one is selected at random, and the probability of choosing box A is double that of box B. If a red ball is drawn from the selected box then the probability that it has come from box B is
- a)21/41
- b)10/31
- c)12/31
- d)13/41
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
Box A contains 2 black and 3 red balls, while box B contains 3 black a...
Solution:
Given: Box A contains 2 black and 3 red balls, while box B contains 3 black and 4 red balls.
Let P(A) and P(B) be the probabilities of selecting box A and box B, respectively.
Given: The probability of choosing box A is double that of box B.
So, P(A) = 2P(B)
Let E be the event of drawing a red ball from the selected box.
We need to find the probability that the red ball has come from box B given that it is drawn.
Let P(E|A) and P(E|B) be the conditional probabilities of drawing a red ball from box A and box B, respectively.
P(E|A) = 3/5, as box A contains 3 red balls out of 5 balls in total.
P(E|B) = 4/7, as box B contains 4 red balls out of 7 balls in total.
Using Bayes' theorem, we can find the required probability:
P(B|E) = P(E|B) * P(B) / [P(E|A) * P(A) + P(E|B) * P(B)]
P(A) = 2P(B)
=> P(B) = P(A) / 2
=> P(B) = 2/3 and P(A) = 4/3
Putting the values in Bayes' theorem:
P(B|E) = (4/7) * (2/3) / [(3/5) * (4/3) + (4/7) * (2/3)]
P(B|E) = 10/31
Therefore, the probability that the red ball has come from box B given that it is drawn is 10/31.
Hence, option (B) is the correct answer.
Given: Box A contains 2 black and 3 red balls, while box B contains 3 black and 4 red balls.
Let P(A) and P(B) be the probabilities of selecting box A and box B, respectively.
Given: The probability of choosing box A is double that of box B.
So, P(A) = 2P(B)
Let E be the event of drawing a red ball from the selected box.
We need to find the probability that the red ball has come from box B given that it is drawn.
Let P(E|A) and P(E|B) be the conditional probabilities of drawing a red ball from box A and box B, respectively.
P(E|A) = 3/5, as box A contains 3 red balls out of 5 balls in total.
P(E|B) = 4/7, as box B contains 4 red balls out of 7 balls in total.
Using Bayes' theorem, we can find the required probability:
P(B|E) = P(E|B) * P(B) / [P(E|A) * P(A) + P(E|B) * P(B)]
P(A) = 2P(B)
=> P(B) = P(A) / 2
=> P(B) = 2/3 and P(A) = 4/3
Putting the values in Bayes' theorem:
P(B|E) = (4/7) * (2/3) / [(3/5) * (4/3) + (4/7) * (2/3)]
P(B|E) = 10/31
Therefore, the probability that the red ball has come from box B given that it is drawn is 10/31.
Hence, option (B) is the correct answer.
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
|
|
Similar JEE Doubts
Top Courses for JEEView all
Box A contains 2 black and 3 red balls, while box B contains 3 black and 4 red balls. Out of these two boxes one is selected at random, and the probability of choosing box A is double that of box B. If a red ball is drawn from the selected box then the probability that it has come from box B isa)21/41b)10/31c)12/31d)13/41Correct answer is option 'B'. Can you explain this answer?
Question Description
Box A contains 2 black and 3 red balls, while box B contains 3 black and 4 red balls. Out of these two boxes one is selected at random, and the probability of choosing box A is double that of box B. If a red ball is drawn from the selected box then the probability that it has come from box B isa)21/41b)10/31c)12/31d)13/41Correct answer is option 'B'. 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 Box A contains 2 black and 3 red balls, while box B contains 3 black and 4 red balls. Out of these two boxes one is selected at random, and the probability of choosing box A is double that of box B. If a red ball is drawn from the selected box then the probability that it has come from box B isa)21/41b)10/31c)12/31d)13/41Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Box A contains 2 black and 3 red balls, while box B contains 3 black and 4 red balls. Out of these two boxes one is selected at random, and the probability of choosing box A is double that of box B. If a red ball is drawn from the selected box then the probability that it has come from box B isa)21/41b)10/31c)12/31d)13/41Correct answer is option 'B'. Can you explain this answer?.
Box A contains 2 black and 3 red balls, while box B contains 3 black and 4 red balls. Out of these two boxes one is selected at random, and the probability of choosing box A is double that of box B. If a red ball is drawn from the selected box then the probability that it has come from box B isa)21/41b)10/31c)12/31d)13/41Correct answer is option 'B'. 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 Box A contains 2 black and 3 red balls, while box B contains 3 black and 4 red balls. Out of these two boxes one is selected at random, and the probability of choosing box A is double that of box B. If a red ball is drawn from the selected box then the probability that it has come from box B isa)21/41b)10/31c)12/31d)13/41Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Box A contains 2 black and 3 red balls, while box B contains 3 black and 4 red balls. Out of these two boxes one is selected at random, and the probability of choosing box A is double that of box B. If a red ball is drawn from the selected box then the probability that it has come from box B isa)21/41b)10/31c)12/31d)13/41Correct answer is option 'B'. Can you explain this answer?.
Solutions for Box A contains 2 black and 3 red balls, while box B contains 3 black and 4 red balls. Out of these two boxes one is selected at random, and the probability of choosing box A is double that of box B. If a red ball is drawn from the selected box then the probability that it has come from box B isa)21/41b)10/31c)12/31d)13/41Correct 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 Box A contains 2 black and 3 red balls, while box B contains 3 black and 4 red balls. Out of these two boxes one is selected at random, and the probability of choosing box A is double that of box B. If a red ball is drawn from the selected box then the probability that it has come from box B isa)21/41b)10/31c)12/31d)13/41Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Box A contains 2 black and 3 red balls, while box B contains 3 black and 4 red balls. Out of these two boxes one is selected at random, and the probability of choosing box A is double that of box B. If a red ball is drawn from the selected box then the probability that it has come from box B isa)21/41b)10/31c)12/31d)13/41Correct answer is option 'B'. Can you explain this answer?, a detailed solution for Box A contains 2 black and 3 red balls, while box B contains 3 black and 4 red balls. Out of these two boxes one is selected at random, and the probability of choosing box A is double that of box B. If a red ball is drawn from the selected box then the probability that it has come from box B isa)21/41b)10/31c)12/31d)13/41Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of Box A contains 2 black and 3 red balls, while box B contains 3 black and 4 red balls. Out of these two boxes one is selected at random, and the probability of choosing box A is double that of box B. If a red ball is drawn from the selected box then the probability that it has come from box B isa)21/41b)10/31c)12/31d)13/41Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Box A contains 2 black and 3 red balls, while box B contains 3 black and 4 red balls. Out of these two boxes one is selected at random, and the probability of choosing box A is double that of box B. If a red ball is drawn from the selected box then the probability that it has come from box B isa)21/41b)10/31c)12/31d)13/41Correct answer is option 'B'. 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