Multiple choice

A bag contains 12 balls out of which x balls are white. (i) If one ball is drawn at random, what is the probability that it will be a white ball. (ii) If 6 more white balls are put in the bag and if the probability of drawing a white ball will be twice that of in (i), then find x.

  1. (i) $\dfrac{1}{4}$    (ii) $3$ 
  2. (i) $\dfrac{1}{3}$    (ii) $3$ 
  3. (i) $\dfrac{1}{5}$    (ii) $3$ 

  4. None of these
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A Correct answer
Explanation

For (i), the probability is x/12. For (ii), the new number of white balls is x + 6 and total balls is 18. The probability is (x + 6)/18. Given (x + 6)/18 = 2 * (x/12), we get (x + 6)/18 = x/6, so x + 6 = 3x, 2x = 6, x = 3. The probability in (i) is 3/12 = 1/4.

AI explanation

For the first part, the probability of drawing a white ball from the original 12 balls is x divided by 12, and testing the provided value of x as 3 gives a probability of 3/12, which simplifies to 1/4. For the second part, if 6 more white balls are added, the total becomes 18 balls and the new count of white balls is x plus 6, making the new probability (x+6)/18; this is stated to be twice the original probability, so (x+6)/18 equals 2 multiplied by (x/12). Solving this equation, (x+6)/18 equals x/6, which leads to x+6 equaling 3x, yielding x as 3. The results are 1/4 for the first part and 3 for the second part.

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