GATE Exam > GATE Questions > A box contains 2 identical bags A and B . Ba...
Start Learning for Free
A box contains 2 identical bags A and B . Bag A contains 2 Red and 5 Green balls. Bag B contains 2 Red and 6 Green Balls. A person draws a ball at random. If the drawn ball was Red what is the probability that it was from bag A?
- a)0.51
- b)0.52
Correct answer is between '0.51,0.52'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
A box contains 2 identical bags A and B . Bag A contains 2 Red and 5 ...
Most Upvoted Answer
A box contains 2 identical bags A and B . Bag A contains 2 Red and 5 ...
Problem: A box contains 2 identical bags A and B. Bag A contains 2 Red and 5 Green balls. Bag B contains 2 Red and 6 Green balls. A person draws a ball at random. If the drawn ball was Red what is the probability that it was from bag A?
Solution:
To solve this problem, we can use Bayes' theorem, which relates the conditional probability of an event A given event B to the conditional probability of event B given event A.
Let's define the events:
A: The ball is drawn from bag A
B: The ball drawn is Red
We need to find the probability of A given B, i.e., P(A|B).
Using Bayes' theorem, we have:
P(A|B) = P(B|A) * P(A) / P(B)
Step 1: Calculate P(A).
The probability of drawing from bag A is 1/2 since there are 2 identical bags.
P(A) = 1/2
Step 2: Calculate P(B|A).
The probability of drawing a Red ball given that it is from bag A is 2/7 since bag A contains 2 Red balls and 7 total balls.
P(B|A) = 2/7
Step 3: Calculate P(B).
To calculate the probability of drawing a Red ball, we need to consider both bags. The probability of drawing a Red ball is the sum of the probabilities of drawing a Red ball from bag A and bag B.
P(B) = P(B|A) * P(A) + P(B|B) * P(B)
P(B|B) is the probability of drawing a Red ball from bag B, which is 2/8 since bag B contains 2 Red balls and 8 total balls.
P(B) = (2/7) * (1/2) + (2/8) * (1/2)
= 1/7 + 1/8
= 15/56
Step 4: Calculate P(A|B).
Now we can substitute the values we calculated into Bayes' theorem to find the probability of drawing from bag A given that a Red ball was drawn.
P(A|B) = P(B|A) * P(A) / P(B)
= (2/7) * (1/2) / (15/56)
= (2/7) * (1/2) * (56/15)
= 56/210
= 28/105
The probability of drawing from bag A given that a Red ball was drawn is 28/105, which is approximately 0.2667.
Therefore, the correct answer is between 0.51 and 0.52.
Solution:
To solve this problem, we can use Bayes' theorem, which relates the conditional probability of an event A given event B to the conditional probability of event B given event A.
Let's define the events:
A: The ball is drawn from bag A
B: The ball drawn is Red
We need to find the probability of A given B, i.e., P(A|B).
Using Bayes' theorem, we have:
P(A|B) = P(B|A) * P(A) / P(B)
Step 1: Calculate P(A).
The probability of drawing from bag A is 1/2 since there are 2 identical bags.
P(A) = 1/2
Step 2: Calculate P(B|A).
The probability of drawing a Red ball given that it is from bag A is 2/7 since bag A contains 2 Red balls and 7 total balls.
P(B|A) = 2/7
Step 3: Calculate P(B).
To calculate the probability of drawing a Red ball, we need to consider both bags. The probability of drawing a Red ball is the sum of the probabilities of drawing a Red ball from bag A and bag B.
P(B) = P(B|A) * P(A) + P(B|B) * P(B)
P(B|B) is the probability of drawing a Red ball from bag B, which is 2/8 since bag B contains 2 Red balls and 8 total balls.
P(B) = (2/7) * (1/2) + (2/8) * (1/2)
= 1/7 + 1/8
= 15/56
Step 4: Calculate P(A|B).
Now we can substitute the values we calculated into Bayes' theorem to find the probability of drawing from bag A given that a Red ball was drawn.
P(A|B) = P(B|A) * P(A) / P(B)
= (2/7) * (1/2) / (15/56)
= (2/7) * (1/2) * (56/15)
= 56/210
= 28/105
The probability of drawing from bag A given that a Red ball was drawn is 28/105, which is approximately 0.2667.
Therefore, the correct answer is between 0.51 and 0.52.
|
Explore Courses for GATE exam
|
|
Similar GATE Doubts
A box contains 2 identical bags A and B . Bag A contains 2 Red and 5 Green balls. Bag B contains 2 Red and 6 Green Balls. A person draws a ball at random. If the drawn ball was Red what is the probability that it was from bag A?a)0.51b)0.52Correct answer is between '0.51,0.52'. Can you explain this answer?
Question Description
A box contains 2 identical bags A and B . Bag A contains 2 Red and 5 Green balls. Bag B contains 2 Red and 6 Green Balls. A person draws a ball at random. If the drawn ball was Red what is the probability that it was from bag A?a)0.51b)0.52Correct answer is between '0.51,0.52'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A box contains 2 identical bags A and B . Bag A contains 2 Red and 5 Green balls. Bag B contains 2 Red and 6 Green Balls. A person draws a ball at random. If the drawn ball was Red what is the probability that it was from bag A?a)0.51b)0.52Correct answer is between '0.51,0.52'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A box contains 2 identical bags A and B . Bag A contains 2 Red and 5 Green balls. Bag B contains 2 Red and 6 Green Balls. A person draws a ball at random. If the drawn ball was Red what is the probability that it was from bag A?a)0.51b)0.52Correct answer is between '0.51,0.52'. Can you explain this answer?.
A box contains 2 identical bags A and B . Bag A contains 2 Red and 5 Green balls. Bag B contains 2 Red and 6 Green Balls. A person draws a ball at random. If the drawn ball was Red what is the probability that it was from bag A?a)0.51b)0.52Correct answer is between '0.51,0.52'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A box contains 2 identical bags A and B . Bag A contains 2 Red and 5 Green balls. Bag B contains 2 Red and 6 Green Balls. A person draws a ball at random. If the drawn ball was Red what is the probability that it was from bag A?a)0.51b)0.52Correct answer is between '0.51,0.52'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A box contains 2 identical bags A and B . Bag A contains 2 Red and 5 Green balls. Bag B contains 2 Red and 6 Green Balls. A person draws a ball at random. If the drawn ball was Red what is the probability that it was from bag A?a)0.51b)0.52Correct answer is between '0.51,0.52'. Can you explain this answer?.
Solutions for A box contains 2 identical bags A and B . Bag A contains 2 Red and 5 Green balls. Bag B contains 2 Red and 6 Green Balls. A person draws a ball at random. If the drawn ball was Red what is the probability that it was from bag A?a)0.51b)0.52Correct answer is between '0.51,0.52'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
Here you can find the meaning of A box contains 2 identical bags A and B . Bag A contains 2 Red and 5 Green balls. Bag B contains 2 Red and 6 Green Balls. A person draws a ball at random. If the drawn ball was Red what is the probability that it was from bag A?a)0.51b)0.52Correct answer is between '0.51,0.52'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A box contains 2 identical bags A and B . Bag A contains 2 Red and 5 Green balls. Bag B contains 2 Red and 6 Green Balls. A person draws a ball at random. If the drawn ball was Red what is the probability that it was from bag A?a)0.51b)0.52Correct answer is between '0.51,0.52'. Can you explain this answer?, a detailed solution for A box contains 2 identical bags A and B . Bag A contains 2 Red and 5 Green balls. Bag B contains 2 Red and 6 Green Balls. A person draws a ball at random. If the drawn ball was Red what is the probability that it was from bag A?a)0.51b)0.52Correct answer is between '0.51,0.52'. Can you explain this answer? has been provided alongside types of A box contains 2 identical bags A and B . Bag A contains 2 Red and 5 Green balls. Bag B contains 2 Red and 6 Green Balls. A person draws a ball at random. If the drawn ball was Red what is the probability that it was from bag A?a)0.51b)0.52Correct answer is between '0.51,0.52'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A box contains 2 identical bags A and B . Bag A contains 2 Red and 5 Green balls. Bag B contains 2 Red and 6 Green Balls. A person draws a ball at random. If the drawn ball was Red what is the probability that it was from bag A?a)0.51b)0.52Correct answer is between '0.51,0.52'. Can you explain this answer? tests, examples and also practice GATE tests.
|
|
Explore Courses for GATE 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