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There are three boxes with the following composition:
Box I: 5 Red + 7 White + 6 Blue balls
Box III: 3 Red + 4 White + 2 Blue balls
Box II: 4 Red + 8 White + 6 Blue balls
If one ball is drawn at random, then what is the probability that they would be of same?
Box I: 5 Red + 7 White + 6 Blue balls
Box III: 3 Red + 4 White + 2 Blue balls
Box II: 4 Red + 8 White + 6 Blue balls
If one ball is drawn at random, then what is the probability that they would be of same?
Most Upvoted Answer
There are three boxes with the following composition:Box I: 5 Red + 7 ...
Understanding the Problem
To find the probability that the ball drawn from the boxes is of the same color, we first need to calculate the total number of balls in each box and the total number of balls across all boxes.
Composition of Boxes
- Box I:
- Red: 5
- White: 7
- Blue: 6
- Total in Box I: 5 + 7 + 6 = 18 balls
- Box II:
- Red: 4
- White: 8
- Blue: 6
- Total in Box II: 4 + 8 + 6 = 18 balls
- Box III:
- Red: 3
- White: 4
- Blue: 2
- Total in Box III: 3 + 4 + 2 = 9 balls
Total Balls in All Boxes
- Total in all boxes:
- Box I: 18
- Box II: 18
- Box III: 9
- Grand Total: 18 + 18 + 9 = 45 balls
Calculating the Probability
Now, we calculate the probability of drawing a ball of the same color:
- Red Balls:
- Total Red = 5 (Box I) + 4 (Box II) + 3 (Box III) = 12
- White Balls:
- Total White = 7 (Box I) + 8 (Box II) + 4 (Box III) = 19
- Blue Balls:
- Total Blue = 6 (Box I) + 6 (Box II) + 2 (Box III) = 14
Final Calculation
- Total Same Color Balls: 12 (Red) + 19 (White) + 14 (Blue) = 45
The probability of drawing a ball of the same color from any box is:
- Probability = Total Same Color Balls / Grand Total of Balls = 45 / 45 = 1
Conclusion
The probability of drawing a ball of the same color is 1, meaning it is certain that a ball drawn will match the color condition.
To find the probability that the ball drawn from the boxes is of the same color, we first need to calculate the total number of balls in each box and the total number of balls across all boxes.
Composition of Boxes
- Box I:
- Red: 5
- White: 7
- Blue: 6
- Total in Box I: 5 + 7 + 6 = 18 balls
- Box II:
- Red: 4
- White: 8
- Blue: 6
- Total in Box II: 4 + 8 + 6 = 18 balls
- Box III:
- Red: 3
- White: 4
- Blue: 2
- Total in Box III: 3 + 4 + 2 = 9 balls
Total Balls in All Boxes
- Total in all boxes:
- Box I: 18
- Box II: 18
- Box III: 9
- Grand Total: 18 + 18 + 9 = 45 balls
Calculating the Probability
Now, we calculate the probability of drawing a ball of the same color:
- Red Balls:
- Total Red = 5 (Box I) + 4 (Box II) + 3 (Box III) = 12
- White Balls:
- Total White = 7 (Box I) + 8 (Box II) + 4 (Box III) = 19
- Blue Balls:
- Total Blue = 6 (Box I) + 6 (Box II) + 2 (Box III) = 14
Final Calculation
- Total Same Color Balls: 12 (Red) + 19 (White) + 14 (Blue) = 45
The probability of drawing a ball of the same color from any box is:
- Probability = Total Same Color Balls / Grand Total of Balls = 45 / 45 = 1
Conclusion
The probability of drawing a ball of the same color is 1, meaning it is certain that a ball drawn will match the color condition.
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There are three boxes with the following composition:Box I: 5 Red + 7 White + 6 Blue ballsBox III: 3 Red + 4 White + 2 Blue ballsBox II: 4 Red + 8 White + 6 Blue ballsIf one ball is drawn at random, then what is the probability that they would be of same?
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There are three boxes with the following composition:Box I: 5 Red + 7 White + 6 Blue ballsBox III: 3 Red + 4 White + 2 Blue ballsBox II: 4 Red + 8 White + 6 Blue ballsIf one ball is drawn at random, then what is the probability that they would be of same? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about There are three boxes with the following composition:Box I: 5 Red + 7 White + 6 Blue ballsBox III: 3 Red + 4 White + 2 Blue ballsBox II: 4 Red + 8 White + 6 Blue ballsIf one ball is drawn at random, then what is the probability that they would be of same? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are three boxes with the following composition:Box I: 5 Red + 7 White + 6 Blue ballsBox III: 3 Red + 4 White + 2 Blue ballsBox II: 4 Red + 8 White + 6 Blue ballsIf one ball is drawn at random, then what is the probability that they would be of same?.
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