CAT Exam > CAT Questions > A container contains 6 red balls, 5 yellow b...
Start Learning for Free
A container contains 6 red balls, 5 yellow balls and 8 green balls while a second container contains 7 red balls, 9 yellow balls and 5 green balls. Rakesh picks one ball from each of the two containers. Let P(Same) be the probability that the two balls are of the same color and P(Different) be the probability that the two balls are of different colors. Then, which of the following statements can be concluded:-
- a)2 x P(Same) > P(Different) > P(Same)
- b)3 x P(Same) > P(Different) > 2 x P(Same)
- c)P(Different) > 3 x P(Same)
- d)P(Different) < />
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
A container contains 6 red balls, 5 yellow balls and 8 green balls wh...
Introduction:
In this problem, we are given two containers, each containing balls of three different colors: red, yellow, and green. We need to find the probability that the two balls picked, one from each container, are of the same color (P(Same)) and the probability that they are of different colors (P(Different)). We are then asked to determine which of the given options is correct.
Given Data:
Container 1: 6 red balls, 5 yellow balls, and 8 green balls
Container 2: 7 red balls, 9 yellow balls, and 5 green balls
Calculating Probability:
To calculate the probability, we need to find the total number of possible outcomes and the number of favorable outcomes.
Possible Outcomes:
The number of possible outcomes is given by the product of the number of balls in each container:
Total possible outcomes = Total balls in container 1 × Total balls in container 2
Total possible outcomes = (6 + 5 + 8) × (7 + 9 + 5) = 19 × 21 = 399
Favorable Outcomes for Same Color:
To find the favorable outcomes for the same color, we need to consider the three different cases:
Case 1: Both balls are red
Favorable outcomes = Number of red balls in container 1 × Number of red balls in container 2 = 6 × 7 = 42
Case 2: Both balls are yellow
Favorable outcomes = Number of yellow balls in container 1 × Number of yellow balls in container 2 = 5 × 9 = 45
Case 3: Both balls are green
Favorable outcomes = Number of green balls in container 1 × Number of green balls in container 2 = 8 × 5 = 40
Total favorable outcomes for same color = Sum of favorable outcomes for each case = 42 + 45 + 40 = 127
Calculating Probabilities:
Now, we can calculate the probabilities of same color and different color:
P(Same) = Favorable outcomes for same color / Total possible outcomes = 127 / 399 = 0.318
P(Different) = 1 - P(Same) = 1 - 0.318 = 0.682
Comparing Probabilities:
Now, let's compare the probabilities as given in the options:
a) 2 × P(Same) > P(Different) > P(Same)
2 × 0.318 = 0.636
0.636 > 0.682 > 0.318
This option is not correct because the middle inequality is reversed.
b) 3 × P(Same) > P(Different) > 2 × P(Same)
3 × 0.318 = 0.954
0.954 > 0.682 > 2 × 0.318
This option is correct because all the inequalities hold true.
c) P(Different) > 3 × P(Same)
0.682 > 3 × 0.318 = 0.954
This option is not correct because the inequality is reversed.
d) P(Different) < />
0.682 < 0.318="" />
In this problem, we are given two containers, each containing balls of three different colors: red, yellow, and green. We need to find the probability that the two balls picked, one from each container, are of the same color (P(Same)) and the probability that they are of different colors (P(Different)). We are then asked to determine which of the given options is correct.
Given Data:
Container 1: 6 red balls, 5 yellow balls, and 8 green balls
Container 2: 7 red balls, 9 yellow balls, and 5 green balls
Calculating Probability:
To calculate the probability, we need to find the total number of possible outcomes and the number of favorable outcomes.
Possible Outcomes:
The number of possible outcomes is given by the product of the number of balls in each container:
Total possible outcomes = Total balls in container 1 × Total balls in container 2
Total possible outcomes = (6 + 5 + 8) × (7 + 9 + 5) = 19 × 21 = 399
Favorable Outcomes for Same Color:
To find the favorable outcomes for the same color, we need to consider the three different cases:
Case 1: Both balls are red
Favorable outcomes = Number of red balls in container 1 × Number of red balls in container 2 = 6 × 7 = 42
Case 2: Both balls are yellow
Favorable outcomes = Number of yellow balls in container 1 × Number of yellow balls in container 2 = 5 × 9 = 45
Case 3: Both balls are green
Favorable outcomes = Number of green balls in container 1 × Number of green balls in container 2 = 8 × 5 = 40
Total favorable outcomes for same color = Sum of favorable outcomes for each case = 42 + 45 + 40 = 127
Calculating Probabilities:
Now, we can calculate the probabilities of same color and different color:
P(Same) = Favorable outcomes for same color / Total possible outcomes = 127 / 399 = 0.318
P(Different) = 1 - P(Same) = 1 - 0.318 = 0.682
Comparing Probabilities:
Now, let's compare the probabilities as given in the options:
a) 2 × P(Same) > P(Different) > P(Same)
2 × 0.318 = 0.636
0.636 > 0.682 > 0.318
This option is not correct because the middle inequality is reversed.
b) 3 × P(Same) > P(Different) > 2 × P(Same)
3 × 0.318 = 0.954
0.954 > 0.682 > 2 × 0.318
This option is correct because all the inequalities hold true.
c) P(Different) > 3 × P(Same)
0.682 > 3 × 0.318 = 0.954
This option is not correct because the inequality is reversed.
d) P(Different) < />
0.682 < 0.318="" />
Free Test
FREE
| Start Free Test |
Community Answer
A container contains 6 red balls, 5 yellow balls and 8 green balls wh...
P(Same) = P(Red-1)P(Red-2) + P(Yellow-1)P(Yellow-2) + P(Green-1)P(Green-2) = 6/19 X 7/21 + 5/19 X 9/21 + 8/19 X 5/21 = 42/399 + 45/399 + 40/399 = 127/399
P(Different) = 1 - P(Same) = 1 - 127/399 = 272/399.
Hence, 3 P(Same) > P(Different) > 2 P(Same)
Attention CAT Students!
To make sure you are not studying endlessly, EduRev has designed CAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CAT.
|
Explore Courses for CAT exam
|
|
Similar CAT Doubts
Top Courses for CATView all
A container contains 6 red balls, 5 yellow balls and 8 green balls while a second container contains 7 red balls, 9 yellow balls and 5 green balls. Rakesh picks one ball from each of the two containers. Let P(Same) be the probability that the two balls are of the same color and P(Different) be the probability that the two balls are of different colors. Then, which of the following statements can be concluded:-a)2 x P(Same) > P(Different) > P(Same)b)3 x P(Same) > P(Different) > 2 x P(Same)c)P(Different) > 3 x P(Same)d)P(Different) Correct answer is option 'B'. Can you explain this answer?
Question Description
A container contains 6 red balls, 5 yellow balls and 8 green balls while a second container contains 7 red balls, 9 yellow balls and 5 green balls. Rakesh picks one ball from each of the two containers. Let P(Same) be the probability that the two balls are of the same color and P(Different) be the probability that the two balls are of different colors. Then, which of the following statements can be concluded:-a)2 x P(Same) > P(Different) > P(Same)b)3 x P(Same) > P(Different) > 2 x P(Same)c)P(Different) > 3 x P(Same)d)P(Different) Correct answer is option 'B'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A container contains 6 red balls, 5 yellow balls and 8 green balls while a second container contains 7 red balls, 9 yellow balls and 5 green balls. Rakesh picks one ball from each of the two containers. Let P(Same) be the probability that the two balls are of the same color and P(Different) be the probability that the two balls are of different colors. Then, which of the following statements can be concluded:-a)2 x P(Same) > P(Different) > P(Same)b)3 x P(Same) > P(Different) > 2 x P(Same)c)P(Different) > 3 x P(Same)d)P(Different) Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A container contains 6 red balls, 5 yellow balls and 8 green balls while a second container contains 7 red balls, 9 yellow balls and 5 green balls. Rakesh picks one ball from each of the two containers. Let P(Same) be the probability that the two balls are of the same color and P(Different) be the probability that the two balls are of different colors. Then, which of the following statements can be concluded:-a)2 x P(Same) > P(Different) > P(Same)b)3 x P(Same) > P(Different) > 2 x P(Same)c)P(Different) > 3 x P(Same)d)P(Different) Correct answer is option 'B'. Can you explain this answer?.
A container contains 6 red balls, 5 yellow balls and 8 green balls while a second container contains 7 red balls, 9 yellow balls and 5 green balls. Rakesh picks one ball from each of the two containers. Let P(Same) be the probability that the two balls are of the same color and P(Different) be the probability that the two balls are of different colors. Then, which of the following statements can be concluded:-a)2 x P(Same) > P(Different) > P(Same)b)3 x P(Same) > P(Different) > 2 x P(Same)c)P(Different) > 3 x P(Same)d)P(Different) Correct answer is option 'B'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A container contains 6 red balls, 5 yellow balls and 8 green balls while a second container contains 7 red balls, 9 yellow balls and 5 green balls. Rakesh picks one ball from each of the two containers. Let P(Same) be the probability that the two balls are of the same color and P(Different) be the probability that the two balls are of different colors. Then, which of the following statements can be concluded:-a)2 x P(Same) > P(Different) > P(Same)b)3 x P(Same) > P(Different) > 2 x P(Same)c)P(Different) > 3 x P(Same)d)P(Different) Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A container contains 6 red balls, 5 yellow balls and 8 green balls while a second container contains 7 red balls, 9 yellow balls and 5 green balls. Rakesh picks one ball from each of the two containers. Let P(Same) be the probability that the two balls are of the same color and P(Different) be the probability that the two balls are of different colors. Then, which of the following statements can be concluded:-a)2 x P(Same) > P(Different) > P(Same)b)3 x P(Same) > P(Different) > 2 x P(Same)c)P(Different) > 3 x P(Same)d)P(Different) Correct answer is option 'B'. Can you explain this answer?.
Solutions for A container contains 6 red balls, 5 yellow balls and 8 green balls while a second container contains 7 red balls, 9 yellow balls and 5 green balls. Rakesh picks one ball from each of the two containers. Let P(Same) be the probability that the two balls are of the same color and P(Different) be the probability that the two balls are of different colors. Then, which of the following statements can be concluded:-a)2 x P(Same) > P(Different) > P(Same)b)3 x P(Same) > P(Different) > 2 x P(Same)c)P(Different) > 3 x P(Same)d)P(Different) Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of A container contains 6 red balls, 5 yellow balls and 8 green balls while a second container contains 7 red balls, 9 yellow balls and 5 green balls. Rakesh picks one ball from each of the two containers. Let P(Same) be the probability that the two balls are of the same color and P(Different) be the probability that the two balls are of different colors. Then, which of the following statements can be concluded:-a)2 x P(Same) > P(Different) > P(Same)b)3 x P(Same) > P(Different) > 2 x P(Same)c)P(Different) > 3 x P(Same)d)P(Different) Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A container contains 6 red balls, 5 yellow balls and 8 green balls while a second container contains 7 red balls, 9 yellow balls and 5 green balls. Rakesh picks one ball from each of the two containers. Let P(Same) be the probability that the two balls are of the same color and P(Different) be the probability that the two balls are of different colors. Then, which of the following statements can be concluded:-a)2 x P(Same) > P(Different) > P(Same)b)3 x P(Same) > P(Different) > 2 x P(Same)c)P(Different) > 3 x P(Same)d)P(Different) Correct answer is option 'B'. Can you explain this answer?, a detailed solution for A container contains 6 red balls, 5 yellow balls and 8 green balls while a second container contains 7 red balls, 9 yellow balls and 5 green balls. Rakesh picks one ball from each of the two containers. Let P(Same) be the probability that the two balls are of the same color and P(Different) be the probability that the two balls are of different colors. Then, which of the following statements can be concluded:-a)2 x P(Same) > P(Different) > P(Same)b)3 x P(Same) > P(Different) > 2 x P(Same)c)P(Different) > 3 x P(Same)d)P(Different) Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of A container contains 6 red balls, 5 yellow balls and 8 green balls while a second container contains 7 red balls, 9 yellow balls and 5 green balls. Rakesh picks one ball from each of the two containers. Let P(Same) be the probability that the two balls are of the same color and P(Different) be the probability that the two balls are of different colors. Then, which of the following statements can be concluded:-a)2 x P(Same) > P(Different) > P(Same)b)3 x P(Same) > P(Different) > 2 x P(Same)c)P(Different) > 3 x P(Same)d)P(Different) Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A container contains 6 red balls, 5 yellow balls and 8 green balls while a second container contains 7 red balls, 9 yellow balls and 5 green balls. Rakesh picks one ball from each of the two containers. Let P(Same) be the probability that the two balls are of the same color and P(Different) be the probability that the two balls are of different colors. Then, which of the following statements can be concluded:-a)2 x P(Same) > P(Different) > P(Same)b)3 x P(Same) > P(Different) > 2 x P(Same)c)P(Different) > 3 x P(Same)d)P(Different) Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice CAT tests.
|
|
Explore Courses for CAT 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