JEE Exam > JEE Questions > An urn contains nine balls of which three are...
Start Learning for Free
An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colours is
[AIEEE 2010]
- a)1/3
- b)2/7
- c)1/21
- d)2/23
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
An urn contains nine balls of which three are red, four are blue and t...
Required probability
Most Upvoted Answer
An urn contains nine balls of which three are red, four are blue and t...
Problem:
An urn contains nine balls of which three are red, four are blue, and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colors is?
Solution:
To find the probability that the three balls have different colors, we need to find the total number of favorable outcomes and the total number of possible outcomes.
Step 1: Total number of possible outcomes
When three balls are drawn without replacement, the total number of possible outcomes can be found using combinations. We need to choose 3 balls out of the 9 available balls.
Number of possible outcomes = C(9, 3) = 84
Step 2: Total number of favorable outcomes
For the three balls to have different colors, we can consider the following cases:
Case 1: Red, Blue, Green
- We can choose 1 red ball from the 3 available red balls.
- We can choose 1 blue ball from the 4 available blue balls.
- We can choose 1 green ball from the 2 available green balls.
- Number of favorable outcomes = C(3, 1) * C(4, 1) * C(2, 1) = 3 * 4 * 2 = 24
Case 2: Blue, Red, Green
- We can choose 1 blue ball from the 4 available blue balls.
- We can choose 1 red ball from the 3 available red balls.
- We can choose 1 green ball from the 2 available green balls.
- Number of favorable outcomes = C(4, 1) * C(3, 1) * C(2, 1) = 4 * 3 * 2 = 24
Case 3: Blue, Green, Red
- We can choose 1 blue ball from the 4 available blue balls.
- We can choose 1 green ball from the 2 available green balls.
- We can choose 1 red ball from the 3 available red balls.
- Number of favorable outcomes = C(4, 1) * C(2, 1) * C(3, 1) = 4 * 2 * 3 = 24
Case 4: Green, Blue, Red
- We can choose 1 green ball from the 2 available green balls.
- We can choose 1 blue ball from the 4 available blue balls.
- We can choose 1 red ball from the 3 available red balls.
- Number of favorable outcomes = C(2, 1) * C(4, 1) * C(3, 1) = 2 * 4 * 3 = 24
Total number of favorable outcomes = 24 + 24 + 24 + 24 = 96
Step 3: Calculating probability
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 96 / 84
Probability = 2/7
Therefore, the probability that the three balls have different colors is 2/7.
An urn contains nine balls of which three are red, four are blue, and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colors is?
Solution:
To find the probability that the three balls have different colors, we need to find the total number of favorable outcomes and the total number of possible outcomes.
Step 1: Total number of possible outcomes
When three balls are drawn without replacement, the total number of possible outcomes can be found using combinations. We need to choose 3 balls out of the 9 available balls.
Number of possible outcomes = C(9, 3) = 84
Step 2: Total number of favorable outcomes
For the three balls to have different colors, we can consider the following cases:
Case 1: Red, Blue, Green
- We can choose 1 red ball from the 3 available red balls.
- We can choose 1 blue ball from the 4 available blue balls.
- We can choose 1 green ball from the 2 available green balls.
- Number of favorable outcomes = C(3, 1) * C(4, 1) * C(2, 1) = 3 * 4 * 2 = 24
Case 2: Blue, Red, Green
- We can choose 1 blue ball from the 4 available blue balls.
- We can choose 1 red ball from the 3 available red balls.
- We can choose 1 green ball from the 2 available green balls.
- Number of favorable outcomes = C(4, 1) * C(3, 1) * C(2, 1) = 4 * 3 * 2 = 24
Case 3: Blue, Green, Red
- We can choose 1 blue ball from the 4 available blue balls.
- We can choose 1 green ball from the 2 available green balls.
- We can choose 1 red ball from the 3 available red balls.
- Number of favorable outcomes = C(4, 1) * C(2, 1) * C(3, 1) = 4 * 2 * 3 = 24
Case 4: Green, Blue, Red
- We can choose 1 green ball from the 2 available green balls.
- We can choose 1 blue ball from the 4 available blue balls.
- We can choose 1 red ball from the 3 available red balls.
- Number of favorable outcomes = C(2, 1) * C(4, 1) * C(3, 1) = 2 * 4 * 3 = 24
Total number of favorable outcomes = 24 + 24 + 24 + 24 = 96
Step 3: Calculating probability
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 96 / 84
Probability = 2/7
Therefore, the probability that the three balls have different colors is 2/7.
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
An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colours is[AIEEE 2010]a)1/3b)2/7c)1/21d)2/23Correct answer is option 'B'. Can you explain this answer?
Question Description
An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colours is[AIEEE 2010]a)1/3b)2/7c)1/21d)2/23Correct 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 nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colours is[AIEEE 2010]a)1/3b)2/7c)1/21d)2/23Correct 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 nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colours is[AIEEE 2010]a)1/3b)2/7c)1/21d)2/23Correct answer is option 'B'. Can you explain this answer?.
An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colours is[AIEEE 2010]a)1/3b)2/7c)1/21d)2/23Correct 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 nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colours is[AIEEE 2010]a)1/3b)2/7c)1/21d)2/23Correct 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 nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colours is[AIEEE 2010]a)1/3b)2/7c)1/21d)2/23Correct answer is option 'B'. Can you explain this answer?.
Solutions for An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colours is[AIEEE 2010]a)1/3b)2/7c)1/21d)2/23Correct 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 An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colours is[AIEEE 2010]a)1/3b)2/7c)1/21d)2/23Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colours is[AIEEE 2010]a)1/3b)2/7c)1/21d)2/23Correct answer is option 'B'. Can you explain this answer?, a detailed solution for An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colours is[AIEEE 2010]a)1/3b)2/7c)1/21d)2/23Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colours is[AIEEE 2010]a)1/3b)2/7c)1/21d)2/23Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colours is[AIEEE 2010]a)1/3b)2/7c)1/21d)2/23Correct 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