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There are three boxes with the following composition: Box l: 4 Red 9 White 3 Blue balls Box II: 5 Red 8 White 3 Blue balls Box III: 6 Red 7 White 2 Blue balls If one ball is drawn at random, then what is the probability that they would be of same colour?
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There are three boxes with the following composition: Box l: 4 Red 9...
Probability of Drawing Balls of Same Colour from Three Boxes
Given Information:
- Box I: 4 Red, 9 White, and 3 Blue balls
- Box II: 5 Red, 8 White, and 3 Blue balls
- Box III: 6 Red, 7 White, and 2 Blue balls
Calculating the Probability
To calculate the probability of drawing balls of the same colour, we need to find the total number of balls in all the boxes and the number of balls of each colour.
- Total number of balls in all boxes = 4+9+3+5+8+3+6+7+2 = 47
- Number of Red balls = 4+5+6 = 15
- Number of White balls = 9+8+7 = 24
- Number of Blue balls = 3+3+2 = 8
Now, we can calculate the probability of drawing balls of the same colour:
- Probability of drawing a Red ball = 15/47
- Probability of drawing a White ball = 24/47
- Probability of drawing a Blue ball = 8/47
Since there are three boxes, there are three possible scenarios where we can draw balls of the same colour:
- Scenario 1: Draw three Red balls
- Scenario 2: Draw three White balls
- Scenario 3: Draw three Blue balls
Now, we can calculate the probability of each scenario:
- Probability of Scenario 1 = (15/47) * (14/46) * (13/45) = 0.036
- Probability of Scenario 2 = (24/47) * (23/46) * (22/45) = 0.089
- Probability of Scenario 3 = (8/47) * (7/46) * (6/45) = 0.002
Finally, we can calculate the probability of drawing balls of the same colour by adding the probabilities of all three scenarios:
- Probability of drawing balls of the same colour = 0.036 + 0.089 + 0.002 = 0.127
Conclusion
The probability of drawing balls of the same colour from the three boxes is 0.127 or approximately 12.7%.
Community Answer
There are three boxes with the following composition: Box l: 4 Red 9...
4/16�9/16�3/16 + 5/16�8/16�3/16 +6/15�7/15�2/15 = 92797/1152000
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There are three boxes with the following composition: Box l: 4 Red 9 White 3 Blue balls Box II: 5 Red 8 White 3 Blue balls Box III: 6 Red 7 White 2 Blue balls If one ball is drawn at random, then what is the probability that they would be of same colour?
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