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There are three boxes with the following composition:
Box I: 5 Red + 7 White + 6 Blue balls
Box II: 4 Red + 8 White + 6 Blue balls
Box III: 3 Red + 4 White + 2 Blue balls
If one ball is drawn at random, then what is the probability that they would be of same colour?
- a)89/729
- b)97/729
- c)82/729
- d)23/32
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
There are three boxes with the following composition:Box I: 5 Red + 7 ...
Solution:
To find the probability that the ball drawn is of the same color, we need to find the probability of drawing a red ball or a white ball or a blue ball from any of the three boxes.
Probability of drawing a red ball:
Total red balls = 5 + 4 + 3 = 12
Total number of balls = 5 + 7 + 6 + 4 + 8 + 6 + 3 + 4 + 2 = 45
Therefore, the probability of drawing a red ball = 12/45 = 4/15
Probability of drawing a white ball:
Total white balls = 7 + 8 + 4 = 19
Total number of balls = 5 + 7 + 6 + 4 + 8 + 6 + 3 + 4 + 2 = 45
Therefore, the probability of drawing a white ball = 19/45
Probability of drawing a blue ball:
Total blue balls = 6 + 6 + 2 = 14
Total number of balls = 5 + 7 + 6 + 4 + 8 + 6 + 3 + 4 + 2 = 45
Therefore, the probability of drawing a blue ball = 14/45
Now, we need to find the probability of drawing a ball of the same color, which can be calculated as follows:
Probability of drawing a ball of the same color = Probability of drawing a red ball + Probability of drawing a white ball + Probability of drawing a blue ball
Probability of drawing a ball of the same color = 4/15 + 19/45 + 14/45
Probability of drawing a ball of the same color = 89/225
Simplifying the fraction, we get:
Probability of drawing a ball of the same color = 89/729
Therefore, the correct option is (a) 89/729.
To find the probability that the ball drawn is of the same color, we need to find the probability of drawing a red ball or a white ball or a blue ball from any of the three boxes.
Probability of drawing a red ball:
Total red balls = 5 + 4 + 3 = 12
Total number of balls = 5 + 7 + 6 + 4 + 8 + 6 + 3 + 4 + 2 = 45
Therefore, the probability of drawing a red ball = 12/45 = 4/15
Probability of drawing a white ball:
Total white balls = 7 + 8 + 4 = 19
Total number of balls = 5 + 7 + 6 + 4 + 8 + 6 + 3 + 4 + 2 = 45
Therefore, the probability of drawing a white ball = 19/45
Probability of drawing a blue ball:
Total blue balls = 6 + 6 + 2 = 14
Total number of balls = 5 + 7 + 6 + 4 + 8 + 6 + 3 + 4 + 2 = 45
Therefore, the probability of drawing a blue ball = 14/45
Now, we need to find the probability of drawing a ball of the same color, which can be calculated as follows:
Probability of drawing a ball of the same color = Probability of drawing a red ball + Probability of drawing a white ball + Probability of drawing a blue ball
Probability of drawing a ball of the same color = 4/15 + 19/45 + 14/45
Probability of drawing a ball of the same color = 89/225
Simplifying the fraction, we get:
Probability of drawing a ball of the same color = 89/729
Therefore, the correct option is (a) 89/729.
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Community Answer
There are three boxes with the following composition:Box I: 5 Red + 7 ...
5/18�7/18�6/18 +4/18�8/18�6/18+3/9�4/9�2/9 = 89/729
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There are three boxes with the following composition:Box I: 5 Red + 7 White + 6 Blue ballsBox II: 4 Red + 8 White + 6 Blue ballsBox III: 3 Red + 4 White + 2 Blue ballsIf one ball is drawn at random, then what is the probability that they would be of same colour?a)89/729b)97/729c)82/729d)23/32Correct answer is option 'A'. Can you explain this answer?
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