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A bag contains 12 balls out of which x are white. If one ball is drawn at random, the probability that it will be a white ball is x/12. If 6 more white balls are put in the bag, the probability of drawing a white ball will be double than that obtained in .find x.
- a)3
- b)4
- c)5
- d)6
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A bag contains 12 balls out of which x are white. If one ball is drawn...
Total number of balls = 12
Total number of black balls = x
P (getting a black ball) = x/12
Now if 6 more black balls are put in the box, then
Total number of balls = 12 + 6 = 18
Total number of black balls = x + 6
P (getting a black ball now) = (x+6)/18
According to the condition given in the question
2(x/12) = (x+6)/18
3x = x+6
x = 3
Most Upvoted Answer
A bag contains 12 balls out of which x are white. If one ball is drawn...
To solve this problem, we can use the concept of probability and algebraic equations.
Let's assume that the initial number of white balls in the bag is x.
Probability of drawing a white ball from the bag = Number of white balls / Total number of balls
According to the given information, the probability of drawing a white ball is x/12.
Now, let's calculate the new probability of drawing a white ball after adding 6 more white balls to the bag.
New total number of white balls in the bag = x + 6
New total number of balls in the bag = 12 + 6 = 18
New probability of drawing a white ball = Number of white balls / Total number of balls
New probability of drawing a white ball = (x + 6) / 18
According to the question, the new probability is double the initial probability:
(x + 6) / 18 = 2 * (x/12)
Simplifying the equation:
(x + 6) / 18 = 2x / 12
12(x + 6) = 18(2x)
12x + 72 = 36x
72 = 36x - 12x
72 = 24x
x = 72 / 24
x = 3
Therefore, the initial number of white balls in the bag is 3. Thus, the correct answer is option A.
Let's assume that the initial number of white balls in the bag is x.
Probability of drawing a white ball from the bag = Number of white balls / Total number of balls
According to the given information, the probability of drawing a white ball is x/12.
Now, let's calculate the new probability of drawing a white ball after adding 6 more white balls to the bag.
New total number of white balls in the bag = x + 6
New total number of balls in the bag = 12 + 6 = 18
New probability of drawing a white ball = Number of white balls / Total number of balls
New probability of drawing a white ball = (x + 6) / 18
According to the question, the new probability is double the initial probability:
(x + 6) / 18 = 2 * (x/12)
Simplifying the equation:
(x + 6) / 18 = 2x / 12
12(x + 6) = 18(2x)
12x + 72 = 36x
72 = 36x - 12x
72 = 24x
x = 72 / 24
x = 3
Therefore, the initial number of white balls in the bag is 3. Thus, the correct answer is option A.
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A bag contains 12 balls out of which x are white. If one ball is drawn at random, the probability that it will be a white ball is x/12. If 6 more white balls are put in the bag, the probability of drawing a white ball will be double than that obtained in .find x.a)3b)4c)5d)6Correct answer is option 'A'. Can you explain this answer?
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