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 double of what it was before. Find x

Solution:

We know that,

Probability = Number of possible outcomes / Total number of outcomes

Total Number of balls = 12

Let the number of black balls = x

Probability of getting black ball = Number of possible outcomes / Total number of outcomes

= x/12

If 6 more black balls are put in the box, the probability of drawing a black ball is now double of what it was before,

Total number of balls = 12 + 6

Number of black balls = x + 6

Now,

2 × Probability of drawing black ball before = probability of drawing black ball

2 × Probability of drawing black ball before = Number of possible outcomes /Total number of outcomes

2(x/12) = (x + 6)/18

3x = x + 6

3x - x = 6

2x = 6

x = 3

Hence, previously, the number of black balls was 3.

Thus, the probability of getting a black ball initially was x/12 = 3/12 = 1/4.

Check out more on terms of probability.

☛ Check: NCERT Solutions for Class 10 Maths Chapter 15

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Video Solution:

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 double of what it was before. Find x

NCERT Solutions for Class 10 Maths  Chapter 15 Exercise 15.2 Question 4

Summary:

A box contains 12 balls out of which x are black. If one ball is drawn at random from the box, the probability that it will be a black ball is 1/4. If 6 more black balls are put in the box, the probability of drawing a black ball is now double of what it was before. The value of x is 3.

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