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Directions: A bag has 6 green marbles and 5 red marbles. Two marbles are drawn. If two marbles are drawn simultaneously, then what is the probability of getting two marbles of same color?
- a)6/11
- b)5/11
- c)2/11
- d)7/11
Correct answer is option 'B'. Can you explain this answer?
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Directions: A bag has 6 green marbles and 5 red marbles. Two marbles ...
Probability of getting two marbles of the same color
To find the probability of getting two marbles of the same color, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of possible outcomes
There are a total of 11 marbles in the bag (6 green marbles + 5 red marbles). When two marbles are drawn simultaneously, the total number of possible outcomes is given by the combination formula:
C(n,r) = n! / (r!(n-r)!)
where n is the total number of marbles and r is the number of marbles drawn.
In this case, n = 11 and r = 2. Plugging these values into the formula, we get:
C(11,2) = 11! / (2!(11-2)!)
= 11! / (2!9!)
= (11 * 10 * 9!) / (2! * 9!)
= (11 * 10) / 2
= 55
Therefore, there are a total of 55 possible outcomes when two marbles are drawn.
Number of favorable outcomes
To determine the number of favorable outcomes, we need to consider the cases where both marbles drawn are of the same color.
Case 1: Both marbles are green
There are 6 green marbles in the bag. When two green marbles are drawn, the number of favorable outcomes is given by the combination formula:
C(6,2) = 6! / (2!(6-2)!)
= 6! / (2!4!)
= (6 * 5) / 2
= 15
Case 2: Both marbles are red
Similarly, there are 5 red marbles in the bag. When two red marbles are drawn, the number of favorable outcomes is also given by the combination formula:
C(5,2) = 5! / (2!(5-2)!)
= 5! / (2!3!)
= (5 * 4) / 2
= 10
Therefore, the total number of favorable outcomes is 15 + 10 = 25.
Probability
Finally, we can calculate the probability of getting two marbles of the same color by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
= 25 / 55
= 5 / 11
Therefore, the probability of getting two marbles of the same color is 5/11, which corresponds to option B.
To find the probability of getting two marbles of the same color, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of possible outcomes
There are a total of 11 marbles in the bag (6 green marbles + 5 red marbles). When two marbles are drawn simultaneously, the total number of possible outcomes is given by the combination formula:
C(n,r) = n! / (r!(n-r)!)
where n is the total number of marbles and r is the number of marbles drawn.
In this case, n = 11 and r = 2. Plugging these values into the formula, we get:
C(11,2) = 11! / (2!(11-2)!)
= 11! / (2!9!)
= (11 * 10 * 9!) / (2! * 9!)
= (11 * 10) / 2
= 55
Therefore, there are a total of 55 possible outcomes when two marbles are drawn.
Number of favorable outcomes
To determine the number of favorable outcomes, we need to consider the cases where both marbles drawn are of the same color.
Case 1: Both marbles are green
There are 6 green marbles in the bag. When two green marbles are drawn, the number of favorable outcomes is given by the combination formula:
C(6,2) = 6! / (2!(6-2)!)
= 6! / (2!4!)
= (6 * 5) / 2
= 15
Case 2: Both marbles are red
Similarly, there are 5 red marbles in the bag. When two red marbles are drawn, the number of favorable outcomes is also given by the combination formula:
C(5,2) = 5! / (2!(5-2)!)
= 5! / (2!3!)
= (5 * 4) / 2
= 10
Therefore, the total number of favorable outcomes is 15 + 10 = 25.
Probability
Finally, we can calculate the probability of getting two marbles of the same color by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
= 25 / 55
= 5 / 11
Therefore, the probability of getting two marbles of the same color is 5/11, which corresponds to option B.
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Community Answer
Directions: A bag has 6 green marbles and 5 red marbles. Two marbles ...
The possible results are
GG or RR
Total cases = 11C2
Number of ways in which 2 marbles can be selected from 6 green marbles = 6C2
Number of ways in which 2 marbles can be selected from 5 red marbles = 5C2
Required probability = 
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Directions: A bag has 6 green marbles and 5 red marbles. Two marbles are drawn. If two marbles are drawn simultaneously, then what is the probability of getting two marbles of same color?a)6/11b)5/11c)2/11d)7/11Correct answer is option 'B'. Can you explain this answer?
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Directions: A bag has 6 green marbles and 5 red marbles. Two marbles are drawn. If two marbles are drawn simultaneously, then what is the probability of getting two marbles of same color?a)6/11b)5/11c)2/11d)7/11Correct 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 Directions: A bag has 6 green marbles and 5 red marbles. Two marbles are drawn. If two marbles are drawn simultaneously, then what is the probability of getting two marbles of same color?a)6/11b)5/11c)2/11d)7/11Correct 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 Directions: A bag has 6 green marbles and 5 red marbles. Two marbles are drawn. If two marbles are drawn simultaneously, then what is the probability of getting two marbles of same color?a)6/11b)5/11c)2/11d)7/11Correct answer is option 'B'. Can you explain this answer?.
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