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A bag contains 4 red balls, 6 green balls and 5 blue balls. If three balls are picked at random, what is the probability that two of them are green and one of them is blue in colour?
- a)20/91
- b)10/91
- c)15/91
- d)5/91
- e)25/91
Correct answer is option 'C'. Can you explain this answer?
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To solve this probability problem, we need to first calculate the total number of ways to pick three balls from the bag, and then determine the number of favorable outcomes where two balls are green and one ball is blue.
Total number of ways to pick three balls from the bag:
To calculate the total number of ways to pick three balls from the bag, we can use the concept of combinations. The total number of balls in the bag is 4 + 6 + 5 = 15. Therefore, the total number of ways to pick three balls from the bag is given by the combination formula:
C(15, 3) = 15! / (3!(15-3)!) = 15! / (3!12!) = (15*14*13) / (3*2*1) = 455
Favorable outcomes where two balls are green and one ball is blue:
To calculate the number of favorable outcomes, we need to consider that there are 6 green balls and 5 blue balls in the bag. We need to choose 2 green balls from the 6 available and 1 blue ball from the 5 available. Therefore, the number of favorable outcomes is given by the product of the combinations:
C(6, 2) * C(5, 1) = (6! / (2!(6-2)!)) * (5! / (1!(5-1)!)) = (6*5/2*1) * (5/1) = 15 * 5 = 75
Probability calculation:
The probability is given by the ratio of the number of favorable outcomes to the total number of possible outcomes:
P(two green and one blue) = favorable outcomes / total outcomes = 75 / 455
Simplifying the fraction:
P(two green and one blue) = 15 / 91
The correct option is C) 15/91.
Total number of ways to pick three balls from the bag:
To calculate the total number of ways to pick three balls from the bag, we can use the concept of combinations. The total number of balls in the bag is 4 + 6 + 5 = 15. Therefore, the total number of ways to pick three balls from the bag is given by the combination formula:
C(15, 3) = 15! / (3!(15-3)!) = 15! / (3!12!) = (15*14*13) / (3*2*1) = 455
Favorable outcomes where two balls are green and one ball is blue:
To calculate the number of favorable outcomes, we need to consider that there are 6 green balls and 5 blue balls in the bag. We need to choose 2 green balls from the 6 available and 1 blue ball from the 5 available. Therefore, the number of favorable outcomes is given by the product of the combinations:
C(6, 2) * C(5, 1) = (6! / (2!(6-2)!)) * (5! / (1!(5-1)!)) = (6*5/2*1) * (5/1) = 15 * 5 = 75
Probability calculation:
The probability is given by the ratio of the number of favorable outcomes to the total number of possible outcomes:
P(two green and one blue) = favorable outcomes / total outcomes = 75 / 455
Simplifying the fraction:
P(two green and one blue) = 15 / 91
The correct option is C) 15/91.
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A bag contains 4 red balls, 6 green balls and 5 blue balls. If three balls are picked at random, what is the probability that two of them are green and one of them is blue in colour?a)20/91b)10/91c)15/91d)5/91e)25/91Correct answer is option 'C'. Can you explain this answer?
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A bag contains 4 red balls, 6 green balls and 5 blue balls. If three balls are picked at random, what is the probability that two of them are green and one of them is blue in colour?a)20/91b)10/91c)15/91d)5/91e)25/91Correct answer is option 'C'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A bag contains 4 red balls, 6 green balls and 5 blue balls. If three balls are picked at random, what is the probability that two of them are green and one of them is blue in colour?a)20/91b)10/91c)15/91d)5/91e)25/91Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bag contains 4 red balls, 6 green balls and 5 blue balls. If three balls are picked at random, what is the probability that two of them are green and one of them is blue in colour?a)20/91b)10/91c)15/91d)5/91e)25/91Correct answer is option 'C'. Can you explain this answer?.
A bag contains 4 red balls, 6 green balls and 5 blue balls. If three balls are picked at random, what is the probability that two of them are green and one of them is blue in colour?a)20/91b)10/91c)15/91d)5/91e)25/91Correct answer is option 'C'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A bag contains 4 red balls, 6 green balls and 5 blue balls. If three balls are picked at random, what is the probability that two of them are green and one of them is blue in colour?a)20/91b)10/91c)15/91d)5/91e)25/91Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bag contains 4 red balls, 6 green balls and 5 blue balls. If three balls are picked at random, what is the probability that two of them are green and one of them is blue in colour?a)20/91b)10/91c)15/91d)5/91e)25/91Correct answer is option 'C'. Can you explain this answer?.
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