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Question 4
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

There are 12 balls in the box.
Therefore, total number of outcomes = 12
The number of favourable outcomes = x
Therefore,  P (getting a black ball)
 P1=x12

If 6 more balls put in the box, then,
Total number of outcomes = 12 + 6 = 18
And the number of favourable outcomes = x + 6
So, P (getting a black ball)
P2=x+618

According to question,
P2=2(P1)
x+618=2×x12 
3x=x+6
2x=6
x=3

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