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Direction: Given below are two quantities named A and B. Based on the given information you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers.
There are 5 Red balls, 4 Green balls and 3 Blue balls in a bag. Four balls are drawn at random.
Quantity A: What is the probability that out of these 4 balls, 2 are Red and 2 are Green balls?
Quantity B: What is the probability that out of these 4 balls, 2 are Red, 1 is Green and 1 is Blue ball?
  • a)
    Quantity A > Quantity B
  • b)
    Quantity A < Quantity B
  • c)
    Quantity A ≥ Quantity B
  • d)
    Quantity A ≤ Quantity B
  • e)
    Quantity A = Quantity B or No relation
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Direction: Given below are two quantities named A and B. Based on the ...
5 Red balls, 4 Green balls and 3 Blue balls:
Quantity A:
Probability that 2 are Red and 2 are Green ball = (5C2 × 4C2) /12C4 = 60/495 = 4/33
Quantity B:
Probability that 2 are Red, 1 is Green and 1 is Blue ball = (5C2 × 4C1 × 3C1) /12C4 = 120/495 = 8/33
∴ Quantity A < Quantity B
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Community Answer
Direction: Given below are two quantities named A and B. Based on the ...
Understanding the Problem
We have a bag containing:
- 5 Red balls
- 4 Green balls
- 3 Blue balls
We need to calculate two probabilities:
1. Probability of drawing 2 Red and 2 Green balls.
2. Probability of drawing 2 Red, 1 Green, and 1 Blue ball.
Calculating Quantity A
To find the probability for Quantity A (2 Red and 2 Green):
- Total ways to choose 4 balls from 12: C(12, 4)
- Ways to choose 2 Red from 5: C(5, 2)
- Ways to choose 2 Green from 4: C(4, 2)
Using combination formulas:
- Total ways = C(12, 4)
- Ways for 2 Red = C(5, 2) = 10
- Ways for 2 Green = C(4, 2) = 6
Thus, Probability A = (C(5, 2) * C(4, 2)) / C(12, 4) = (10 * 6) / C(12, 4)
Calculating Quantity B
To find the probability for Quantity B (2 Red, 1 Green, and 1 Blue):
- Ways to choose 2 Red from 5: C(5, 2)
- Ways to choose 1 Green from 4: C(4, 1)
- Ways to choose 1 Blue from 3: C(3, 1)
Thus, Probability B = (C(5, 2) * C(4, 1) * C(3, 1)) / C(12, 4) = (10 * 4 * 3) / C(12, 4)
Comparing the Probabilities
- Probability A = (10 * 6) / C(12, 4)
- Probability B = (10 * 4 * 3) / C(12, 4)
Calculating:
- Probability A = 60 / C(12, 4)
- Probability B = 120 / C(12, 4)
Since 60 < />
Conclusion
Therefore, Quantity A < quantity="" b,="" leading="" us="" to="" the="" correct="" answer:="" />
Option B: Quantity A < quantity="" />
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Direction: Given below are two quantities named A and B. Based on the given information you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers.There are 5 Red balls, 4 Green balls and 3 Blue balls in a bag. Four balls are drawn at random.Quantity A: What is the probability that out of these 4 balls, 2 are Red and 2 are Green balls?Quantity B: What is the probability that out of these 4 balls, 2 are Red, 1 is Green and 1 is Blue ball?a)Quantity A > Quantity Bb)Quantity A < Quantity Bc)Quantity A ≥ Quantity Bd)Quantity A ≤ Quantity Be)Quantity A = Quantity B or No relationCorrect answer is option 'B'. Can you explain this answer?
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