Question

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 balls are put in the box, the probability of drawing a black ball is now
double of what it was before. Find x.
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Answer 1

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Total = 12 (No. of balls )

Events = x, 12-x

$pro bability = \frac{event}{total \: observation}$

Φ Probability of black balls

Black balls = x, Total = 12

$probability = \frac{x}{12}$

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Total = 12+6 = 18

probability = x/18

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ΦAccording to Condition.

$\frac{x}{12} = 2( \frac{x}{18} )$

$\frac{x}{12} = \frac{2x}{18}$

$18x = 2x(12)$

$18x = 24x$

$\frac{18}{24} = x$

$\frac{3}{4} = x$

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Answer 2

Answer:

x = 3

Step-by-step explanation:

x = black balls

12-x = remaining balls

According to question

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

(x+6)/3 = 2(x/2)

2x+12 = 6x

12 = 4x

x = 3

Black balls = 3

P(Getting black balls) = 3/12

= 1/4