Multiple choice

A box contains $12$ balls out of which $x$ are black. If one ball is drawn at random from the box, what is the probability that it will be a black ball? If $6$ more black balls are put in the box, the probability of drawing a black ball is now doubled of what it was before, find $x$.

  1. $\displaystyle\frac{x}{11};\quad x = 1$
  2. $\displaystyle\frac{x}{12};\quad x = 7$
  3. $\displaystyle\frac{x}{13};\quad x = 9$

  4. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
AI explanation

The initial probability of drawing a black ball is the number of black balls, x, divided by the total balls, 12. After adding 6 more black balls, the new probability is (x + 6) divided by the new total of 18. The problem states this new probability is double the old one, so we set up the equation (x + 6)/18 = 2 times (x/12). Solving this gives (x + 6)/18 = x/6, which simplifies to x + 6 = 3x, meaning x = 3; since none of the provided options state x equals 3, the correct choice is None of these.

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