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An urn contains 5 red and 2 green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red, is :
- a)26/49
- b)32/49
- c)27/49
- d)21/49
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
An urn contains 5 red and 2 green balls. A ball is drawn at random fro...
E1 : Event of drawing a Red ball and placing a green ball in the bag
E2 : Event of drawing a green ball and placing a red ball in the bag
E : Event of drawing a red ball in second draw
E2 : Event of drawing a green ball and placing a red ball in the bag
E : Event of drawing a red ball in second draw
Most Upvoted Answer
An urn contains 5 red and 2 green balls. A ball is drawn at random fro...
Problem Analysis:
We need to find the probability that the second ball drawn from the urn is red. To solve this problem, we can use the concept of conditional probability. Let's break down the problem into smaller parts and analyze each step.
Step 1: Calculate the probability of drawing a green ball in the first draw.
The urn contains a total of 7 balls, out of which 2 are green. Therefore, the probability of drawing a green ball in the first draw is:
P(Green) = Number of green balls / Total number of balls = 2/7
Step 2: Calculate the probability of drawing a red ball in the first draw.
The probability of drawing a red ball in the first draw is simply the complement of drawing a green ball:
P(Red) = 1 - P(Green) = 1 - 2/7 = 5/7
Step 3: Calculate the probability of drawing a red ball in the second draw given that the first ball was green.
When a green ball is drawn in the first draw, a red ball is added to the urn. This means that the total number of balls in the urn becomes 8, with 5 red balls and 3 green balls. Therefore, the probability of drawing a red ball in the second draw given that the first ball was green is:
P(Red|Green) = Number of red balls / Total number of balls = 5/8
Step 4: Calculate the probability of drawing a red ball in the second draw given that the first ball was red.
When a red ball is drawn in the first draw, a green ball is added to the urn. This means that the total number of balls in the urn becomes 8, with 6 red balls and 2 green balls. Therefore, the probability of drawing a red ball in the second draw given that the first ball was red is:
P(Red|Red) = Number of red balls / Total number of balls = 6/8 = 3/4
Step 5: Calculate the overall probability of drawing a red ball in the second draw.
To calculate the overall probability, we need to consider the probabilities of the two possible scenarios: drawing a green ball in the first draw and drawing a red ball in the second draw, and drawing a red ball in the first draw and drawing a red ball in the second draw. We can use the law of total probability to calculate this:
P(Red) = P(Red|Green) * P(Green) + P(Red|Red) * P(Red)
= (5/8) * (2/7) + (3/4) * (5/7)
= 10/56 + 15/28
= 10/56 + 30/56
= 40/56
= 10/14
= 5/7
Solution:
The probability that the second ball drawn from the urn is red is 5/7, which is option B.
We need to find the probability that the second ball drawn from the urn is red. To solve this problem, we can use the concept of conditional probability. Let's break down the problem into smaller parts and analyze each step.
Step 1: Calculate the probability of drawing a green ball in the first draw.
The urn contains a total of 7 balls, out of which 2 are green. Therefore, the probability of drawing a green ball in the first draw is:
P(Green) = Number of green balls / Total number of balls = 2/7
Step 2: Calculate the probability of drawing a red ball in the first draw.
The probability of drawing a red ball in the first draw is simply the complement of drawing a green ball:
P(Red) = 1 - P(Green) = 1 - 2/7 = 5/7
Step 3: Calculate the probability of drawing a red ball in the second draw given that the first ball was green.
When a green ball is drawn in the first draw, a red ball is added to the urn. This means that the total number of balls in the urn becomes 8, with 5 red balls and 3 green balls. Therefore, the probability of drawing a red ball in the second draw given that the first ball was green is:
P(Red|Green) = Number of red balls / Total number of balls = 5/8
Step 4: Calculate the probability of drawing a red ball in the second draw given that the first ball was red.
When a red ball is drawn in the first draw, a green ball is added to the urn. This means that the total number of balls in the urn becomes 8, with 6 red balls and 2 green balls. Therefore, the probability of drawing a red ball in the second draw given that the first ball was red is:
P(Red|Red) = Number of red balls / Total number of balls = 6/8 = 3/4
Step 5: Calculate the overall probability of drawing a red ball in the second draw.
To calculate the overall probability, we need to consider the probabilities of the two possible scenarios: drawing a green ball in the first draw and drawing a red ball in the second draw, and drawing a red ball in the first draw and drawing a red ball in the second draw. We can use the law of total probability to calculate this:
P(Red) = P(Red|Green) * P(Green) + P(Red|Red) * P(Red)
= (5/8) * (2/7) + (3/4) * (5/7)
= 10/56 + 15/28
= 10/56 + 30/56
= 40/56
= 10/14
= 5/7
Solution:
The probability that the second ball drawn from the urn is red is 5/7, which is option B.
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An urn contains 5 red and 2 green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red, is :a)26/49b)32/49c)27/49d)21/49Correct answer is option 'B'. Can you explain this answer?
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An urn contains 5 red and 2 green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red, is :a)26/49b)32/49c)27/49d)21/49Correct 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 An urn contains 5 red and 2 green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red, is :a)26/49b)32/49c)27/49d)21/49Correct 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 An urn contains 5 red and 2 green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red, is :a)26/49b)32/49c)27/49d)21/49Correct answer is option 'B'. Can you explain this answer?.
An urn contains 5 red and 2 green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red, is :a)26/49b)32/49c)27/49d)21/49Correct 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 An urn contains 5 red and 2 green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red, is :a)26/49b)32/49c)27/49d)21/49Correct 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 An urn contains 5 red and 2 green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red, is :a)26/49b)32/49c)27/49d)21/49Correct answer is option 'B'. Can you explain this answer?.
Solutions for An urn contains 5 red and 2 green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red, is :a)26/49b)32/49c)27/49d)21/49Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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An urn contains 5 red and 2 green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red, is :a)26/49b)32/49c)27/49d)21/49Correct answer is option 'B'. Can you explain this answer?, a detailed solution for An urn contains 5 red and 2 green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red, is :a)26/49b)32/49c)27/49d)21/49Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of An urn contains 5 red and 2 green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red, is :a)26/49b)32/49c)27/49d)21/49Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice An urn contains 5 red and 2 green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red, is :a)26/49b)32/49c)27/49d)21/49Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice JEE tests.
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