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A bag contains 12 balls out of which $p$ are green. If 6 more green balls are put in the bag, the probability of drawing a green ball will be doubled, then find $p$ .

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answer is B.

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Detailed Solution

It is given that the total number of balls in a bag is 12 in which p are green.
Total number of green balls = p.
If 6 more green balls are put into the bag, the probability will become double.
For an event A,

P (A) = Number of Possible Outcomes Total Number of Outcomes

.
The probability of getting a green ball before adding 6 green balls is given by,

= p 12

The probability of getting a green ball after adding 6 green balls is given by,

= p + 6 12 + 6 = p + 6 18

New probability is double than the existing probability. So, equating both the probabilities, we get,

p + 6 18 = 2 p 12 12 p + 72 = 36 p 24 p = 72 p = 3

The number of green balls initially is 3.
Hence, option 1 is correct.

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