CA Foundation Exam > CA Foundation Questions > A box contains 2 red, 3 green and 2 blue ball...
Start Learning for Free
A box contains 2 red, 3 green and 2 blue balls. Two bails are drawn at random. What is the probability that none of the balls drawn is blue?
- a)10/21
- b)11/21
- c)2/7
- d)5/7
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
A box contains 2 red, 3 green and 2 blue balls. Two bails are drawn at...
Given:
- Total number of balls = 2 red + 3 green + 2 blue = 7
- Two balls are drawn at random
To find:
- Probability that none of the balls drawn is blue
Solution:
Let's first find the total number of ways to draw 2 balls out of 7:
Total ways = 7C2 = (7 * 6) / (2 * 1) = 21
Now, let's find the number of ways to draw 2 balls such that none of them is blue:
Number of ways = 2C0 * 5C2 + 2C1 * 5C1 + 2C2 * 5C0
- 2C0 * 5C2 represents selecting 0 blue balls out of 2 and 2 green balls out of 3
- 2C1 * 5C1 represents selecting 1 blue ball out of 2 and 1 green ball out of 3 (or 1 red ball out of 2 and 1 green ball out of 3)
- 2C2 * 5C0 represents selecting 2 blue balls out of 2 and 0 green balls out of 3 (or 2 red balls out of 2 and 0 green balls out of 3)
Number of ways = (1 * 10) + (2 * 5) + (1 * 1) = 21
Therefore, the probability of drawing 2 balls such that none of them is blue = (Number of ways to draw 2 balls such that none of them is blue) / (Total ways) = 21/21 = 1
But, we need to find the probability that none of the balls drawn is blue. So, we subtract the probability of drawing 2 blue balls from 1:
Probability that none of the balls drawn is blue = 1 - (Probability of drawing 2 blue balls) = 1 - (Number of ways to draw 2 blue balls / Total ways)
Number of ways to draw 2 blue balls = 2C2 * 5C0 = 1
Probability of drawing 2 blue balls = 1/21
Therefore, Probability that none of the balls drawn is blue = 1 - (1/21) = 20/21
Hence, option A (10/21) is incorrect and the correct answer is option B (11/21).
- Total number of balls = 2 red + 3 green + 2 blue = 7
- Two balls are drawn at random
To find:
- Probability that none of the balls drawn is blue
Solution:
Let's first find the total number of ways to draw 2 balls out of 7:
Total ways = 7C2 = (7 * 6) / (2 * 1) = 21
Now, let's find the number of ways to draw 2 balls such that none of them is blue:
Number of ways = 2C0 * 5C2 + 2C1 * 5C1 + 2C2 * 5C0
- 2C0 * 5C2 represents selecting 0 blue balls out of 2 and 2 green balls out of 3
- 2C1 * 5C1 represents selecting 1 blue ball out of 2 and 1 green ball out of 3 (or 1 red ball out of 2 and 1 green ball out of 3)
- 2C2 * 5C0 represents selecting 2 blue balls out of 2 and 0 green balls out of 3 (or 2 red balls out of 2 and 0 green balls out of 3)
Number of ways = (1 * 10) + (2 * 5) + (1 * 1) = 21
Therefore, the probability of drawing 2 balls such that none of them is blue = (Number of ways to draw 2 balls such that none of them is blue) / (Total ways) = 21/21 = 1
But, we need to find the probability that none of the balls drawn is blue. So, we subtract the probability of drawing 2 blue balls from 1:
Probability that none of the balls drawn is blue = 1 - (Probability of drawing 2 blue balls) = 1 - (Number of ways to draw 2 blue balls / Total ways)
Number of ways to draw 2 blue balls = 2C2 * 5C0 = 1
Probability of drawing 2 blue balls = 1/21
Therefore, Probability that none of the balls drawn is blue = 1 - (1/21) = 20/21
Hence, option A (10/21) is incorrect and the correct answer is option B (11/21).
Free Test
| FREE | Start Free Test |
Community Answer
A box contains 2 red, 3 green and 2 blue balls. Two bails are drawn at...
Given:
- Box contains 2 red, 3 green and 2 blue balls.
- Two balls are drawn at random.
To find:
- Probability that none of the balls drawn is blue.
Solution:
Total number of ways to draw 2 balls out of 7 balls = 7C2 = 21
Let A be the event of drawing a non-blue ball in the first draw and B be the event of drawing a non-blue ball in the second draw.
P(A) = (2 red balls + 3 green balls) / 7 balls = 5/7
P(B | A) = probability of drawing a non-blue ball in the second draw given that a non-blue ball was drawn in the first draw
= (1 red ball + 2 green balls) / 6 balls = 3/6 = 1/2
P(A and B) = P(A) x P(B | A)
= (5/7) x (1/2)
= 5/14
Therefore, the probability of drawing two non-blue balls = P(A and B) = 5/14
The probability of not drawing any blue ball = 1 - probability of drawing at least one blue ball
= 1 - (number of ways to draw 1 blue ball x number of ways to draw 1 non-blue ball) / total number of ways to draw 2 balls
= 1 - (2C1 x 5C1) / 21
= 1 - (10/21)
= 11/21
Answer: The probability that none of the balls drawn is blue is 11/21, which is not among the given options. Therefore, the given answer key must be incorrect.
- Box contains 2 red, 3 green and 2 blue balls.
- Two balls are drawn at random.
To find:
- Probability that none of the balls drawn is blue.
Solution:
Total number of ways to draw 2 balls out of 7 balls = 7C2 = 21
Let A be the event of drawing a non-blue ball in the first draw and B be the event of drawing a non-blue ball in the second draw.
P(A) = (2 red balls + 3 green balls) / 7 balls = 5/7
P(B | A) = probability of drawing a non-blue ball in the second draw given that a non-blue ball was drawn in the first draw
= (1 red ball + 2 green balls) / 6 balls = 3/6 = 1/2
P(A and B) = P(A) x P(B | A)
= (5/7) x (1/2)
= 5/14
Therefore, the probability of drawing two non-blue balls = P(A and B) = 5/14
The probability of not drawing any blue ball = 1 - probability of drawing at least one blue ball
= 1 - (number of ways to draw 1 blue ball x number of ways to draw 1 non-blue ball) / total number of ways to draw 2 balls
= 1 - (2C1 x 5C1) / 21
= 1 - (10/21)
= 11/21
Answer: The probability that none of the balls drawn is blue is 11/21, which is not among the given options. Therefore, the given answer key must be incorrect.
Attention CA Foundation Students!
To make sure you are not studying endlessly, EduRev has designed CA Foundation study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CA Foundation.
|
Explore Courses for CA Foundation exam
|
|
Similar CA Foundation Doubts
Top Courses for CA FoundationView all
A box contains 2 red, 3 green and 2 blue balls. Two bails are drawn at random. What is the probability that none of the balls drawn is blue?a)10/21b)11/21c)2/7d)5/7Correct answer is option 'A'. Can you explain this answer?
Question Description
A box contains 2 red, 3 green and 2 blue balls. Two bails are drawn at random. What is the probability that none of the balls drawn is blue?a)10/21b)11/21c)2/7d)5/7Correct answer is option 'A'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about A box contains 2 red, 3 green and 2 blue balls. Two bails are drawn at random. What is the probability that none of the balls drawn is blue?a)10/21b)11/21c)2/7d)5/7Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A box contains 2 red, 3 green and 2 blue balls. Two bails are drawn at random. What is the probability that none of the balls drawn is blue?a)10/21b)11/21c)2/7d)5/7Correct answer is option 'A'. Can you explain this answer?.
A box contains 2 red, 3 green and 2 blue balls. Two bails are drawn at random. What is the probability that none of the balls drawn is blue?a)10/21b)11/21c)2/7d)5/7Correct answer is option 'A'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about A box contains 2 red, 3 green and 2 blue balls. Two bails are drawn at random. What is the probability that none of the balls drawn is blue?a)10/21b)11/21c)2/7d)5/7Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A box contains 2 red, 3 green and 2 blue balls. Two bails are drawn at random. What is the probability that none of the balls drawn is blue?a)10/21b)11/21c)2/7d)5/7Correct answer is option 'A'. Can you explain this answer?.
Solutions for A box contains 2 red, 3 green and 2 blue balls. Two bails are drawn at random. What is the probability that none of the balls drawn is blue?a)10/21b)11/21c)2/7d)5/7Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for CA Foundation.
Download more important topics, notes, lectures and mock test series for CA Foundation Exam by signing up for free.
Here you can find the meaning of A box contains 2 red, 3 green and 2 blue balls. Two bails are drawn at random. What is the probability that none of the balls drawn is blue?a)10/21b)11/21c)2/7d)5/7Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A box contains 2 red, 3 green and 2 blue balls. Two bails are drawn at random. What is the probability that none of the balls drawn is blue?a)10/21b)11/21c)2/7d)5/7Correct answer is option 'A'. Can you explain this answer?, a detailed solution for A box contains 2 red, 3 green and 2 blue balls. Two bails are drawn at random. What is the probability that none of the balls drawn is blue?a)10/21b)11/21c)2/7d)5/7Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of A box contains 2 red, 3 green and 2 blue balls. Two bails are drawn at random. What is the probability that none of the balls drawn is blue?a)10/21b)11/21c)2/7d)5/7Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A box contains 2 red, 3 green and 2 blue balls. Two bails are drawn at random. What is the probability that none of the balls drawn is blue?a)10/21b)11/21c)2/7d)5/7Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice CA Foundation tests.
|
|
Explore Courses for CA Foundation 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