JEE Exam > JEE Questions > There are two balls in an urn whose colours a...
Start Learning for Free
There are two balls in an urn whose colours are not known (each ball can be either white or black). A white ball is put into the urn. A ball is drawn from the urn. The probability that it is white is
- a)1/4
- b)1/3
- c)2/3
- d)1/6
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
There are two balls in an urn whose colours are not known (each ball c...
Let Ei (0 < i < 2) denote the event that urn contains 'i' white and '(2 – i)' black balls.
Let A denote the event that a white ball is drawn from the urn.
We have P(Ei) = 1/3 for i = 0, 1, 2
P (A|E1) = 1/3, P(A|E2) = 2/3, P(A|E3) = 1.
By the total probability rule,
P(A)= P(E1)P(A|E1) + P(E2)P(A|E2) + P(E3)P(A|E3)
Let A denote the event that a white ball is drawn from the urn.
We have P(Ei) = 1/3 for i = 0, 1, 2
P (A|E1) = 1/3, P(A|E2) = 2/3, P(A|E3) = 1.
By the total probability rule,
P(A)= P(E1)P(A|E1) + P(E2)P(A|E2) + P(E3)P(A|E3)
Most Upvoted Answer
There are two balls in an urn whose colours are not known (each ball c...
Understanding the Problem
In the urn, we have two balls whose colors are unknown, and we add a white ball. We need to determine the probability of drawing a white ball.
Possible Scenarios
Initially, the two balls can be in any of the following combinations:
- Scenario 1: Both balls are white (WW)
- Scenario 2: One ball is white, and one is black (WB)
- Scenario 3: One ball is black, and one is white (BW)
- Scenario 4: Both balls are black (BB)
Calculating Probabilities
Since the color of the two initial balls is unknown, we assume each scenario is equally likely:
- Total Scenarios: 4 (WW, WB, BW, BB)
- Adding a white ball to the urn:
Now let's analyze the probability of drawing a white ball in each scenario:
- Scenario WW: 3 white balls (WW + W) → Probability of drawing white = 3/3 = 1
- Scenario WB or BW: 2 white balls and 1 black ball → Probability of drawing white = 2/3
- Scenario BB: 1 white ball and 2 black balls → Probability of drawing white = 1/3
Calculating Overall Probability
Now, to find the overall probability of drawing a white ball:
- WW: 1/4 * 1 = 1/4
- WB: 1/4 * 2/3 = 1/6
- BW: 1/4 * 2/3 = 1/6
- BB: 1/4 * 1/3 = 1/12
Adding these probabilities gives:
1/4 + 1/6 + 1/6 + 1/12 = 9/12 = 3/4
Now, since we are only interested in the scenarios with at least one white ball (WW, WB, BW):
- Total Probability of scenarios with white = (1/4 + 1/6 + 1/6) = 2/3
Final Answer
Therefore, the probability that the drawn ball is white is 2/3, which matches option 'C'.
In the urn, we have two balls whose colors are unknown, and we add a white ball. We need to determine the probability of drawing a white ball.
Possible Scenarios
Initially, the two balls can be in any of the following combinations:
- Scenario 1: Both balls are white (WW)
- Scenario 2: One ball is white, and one is black (WB)
- Scenario 3: One ball is black, and one is white (BW)
- Scenario 4: Both balls are black (BB)
Calculating Probabilities
Since the color of the two initial balls is unknown, we assume each scenario is equally likely:
- Total Scenarios: 4 (WW, WB, BW, BB)
- Adding a white ball to the urn:
Now let's analyze the probability of drawing a white ball in each scenario:
- Scenario WW: 3 white balls (WW + W) → Probability of drawing white = 3/3 = 1
- Scenario WB or BW: 2 white balls and 1 black ball → Probability of drawing white = 2/3
- Scenario BB: 1 white ball and 2 black balls → Probability of drawing white = 1/3
Calculating Overall Probability
Now, to find the overall probability of drawing a white ball:
- WW: 1/4 * 1 = 1/4
- WB: 1/4 * 2/3 = 1/6
- BW: 1/4 * 2/3 = 1/6
- BB: 1/4 * 1/3 = 1/12
Adding these probabilities gives:
1/4 + 1/6 + 1/6 + 1/12 = 9/12 = 3/4
Now, since we are only interested in the scenarios with at least one white ball (WW, WB, BW):
- Total Probability of scenarios with white = (1/4 + 1/6 + 1/6) = 2/3
Final Answer
Therefore, the probability that the drawn ball is white is 2/3, which matches option 'C'.
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
There are two balls in an urn whose colours are not known (each ball can be either white or black). A white ball is put into the urn. A ball is drawn from the urn. The probability that it is white isa)1/4b)1/3c)2/3d)1/6Correct answer is option 'C'. Can you explain this answer?
Question Description
There are two balls in an urn whose colours are not known (each ball can be either white or black). A white ball is put into the urn. A ball is drawn from the urn. The probability that it is white isa)1/4b)1/3c)2/3d)1/6Correct answer is option 'C'. 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 There are two balls in an urn whose colours are not known (each ball can be either white or black). A white ball is put into the urn. A ball is drawn from the urn. The probability that it is white isa)1/4b)1/3c)2/3d)1/6Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are two balls in an urn whose colours are not known (each ball can be either white or black). A white ball is put into the urn. A ball is drawn from the urn. The probability that it is white isa)1/4b)1/3c)2/3d)1/6Correct answer is option 'C'. Can you explain this answer?.
There are two balls in an urn whose colours are not known (each ball can be either white or black). A white ball is put into the urn. A ball is drawn from the urn. The probability that it is white isa)1/4b)1/3c)2/3d)1/6Correct answer is option 'C'. 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 There are two balls in an urn whose colours are not known (each ball can be either white or black). A white ball is put into the urn. A ball is drawn from the urn. The probability that it is white isa)1/4b)1/3c)2/3d)1/6Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are two balls in an urn whose colours are not known (each ball can be either white or black). A white ball is put into the urn. A ball is drawn from the urn. The probability that it is white isa)1/4b)1/3c)2/3d)1/6Correct answer is option 'C'. Can you explain this answer?.
Solutions for There are two balls in an urn whose colours are not known (each ball can be either white or black). A white ball is put into the urn. A ball is drawn from the urn. The probability that it is white isa)1/4b)1/3c)2/3d)1/6Correct answer is option 'C'. 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 There are two balls in an urn whose colours are not known (each ball can be either white or black). A white ball is put into the urn. A ball is drawn from the urn. The probability that it is white isa)1/4b)1/3c)2/3d)1/6Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
There are two balls in an urn whose colours are not known (each ball can be either white or black). A white ball is put into the urn. A ball is drawn from the urn. The probability that it is white isa)1/4b)1/3c)2/3d)1/6Correct answer is option 'C'. Can you explain this answer?, a detailed solution for There are two balls in an urn whose colours are not known (each ball can be either white or black). A white ball is put into the urn. A ball is drawn from the urn. The probability that it is white isa)1/4b)1/3c)2/3d)1/6Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of There are two balls in an urn whose colours are not known (each ball can be either white or black). A white ball is put into the urn. A ball is drawn from the urn. The probability that it is white isa)1/4b)1/3c)2/3d)1/6Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice There are two balls in an urn whose colours are not known (each ball can be either white or black). A white ball is put into the urn. A ball is drawn from the urn. The probability that it is white isa)1/4b)1/3c)2/3d)1/6Correct answer is option 'C'. 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
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup