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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?
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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.
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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?
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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?.
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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
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