Question

A bag contains 12 balls out of which X balls are red
1) if one ball is drawn at random from the what is the probability that it is red
2) if 6 more red ball airport in the bag the probability of drawing a red ball will be two times the probability of drawing a red ball in the first case find the value of x

Answer 1

Probability = No of favourable outcomes of the event / Total possible outcomes of the event

No.of red balls = x
Total balls initially in the bag = 12

So, the probability that we draw a red ball = x/12

Now,
2) No of red balls after putting additional balls = x+6

Total balls in the bag now = 12+6 = 18

Now,
Probability of taking a red ball out = x+6/18

So, according to the given condition,

x+6/18 = 2*x/12
x+6 / 18 = x/6
x+6 = 3x
2x = 6
x = 3

So, no.of red balls initially in the bag = 3

So, probability of drawing a red ball in the first case = 3/12 = 1/4

Answer 2

Answer:

Solution :-

Let the total number of red balls initially be x

Total number of balls in the box = 12

P(getting a red ball) = x/12

Now, 6 red balls are put in the box, then the total number of balls

= 12 + 6

= 18 balls

Then total number of red balls = (x + 6)

Now,

P(getting a red ball) = (x + 6)/18

According to the question.

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

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

Cross multiplying

⇒ 36x = 12x + 72

⇒ 36x - 12x = 72

⇒ 24x = 72

x = 3

So, initially the number of red balls in the box were 3