Question

a bag contains 6 red balls and some blue balls. if the probability of drawing a blue ball from the bag is twice that of red ball, find the number of blue balls in the bag.

Answer 1

No of red balls = 6
No. of blue balls = x (assumed value)
Total no. of balls = 6 + x
According to the question,

Probability of getting a red ball = 6/6+x
Probability of getting a blue ball = 2(6/6+x)

(As the probability of getting a blue ball is twice as much as the probability of getting a red ball. So 2 is multiplied.)

= 12/6+x

We know that 6 + x is the total no. of balls. So, 12 is the number of blue balls.

Hence, the total no of blue balls are 12.

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Answer 2

No of red balls = 6

No of blue balls = x

Total balls = x+6

Probability of getting a blue ball is double of getting a red ball

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

x ( x +6 ) = 6(x+6) * 2

x^2 + 6x = 6x + 36 * 2

x^2 = 36 *2

x = √36 * 2

x = 6 * 2

x = 12