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A box contains black and white balls, such that the probability of picking a black ball is 3/11. When 8 more black balls are added to the box, the probability of picking a black ball becomes 5/13. Find the number of white balls in the box.

A box contains black and white balls, such that the probability of picking a black ball is 3/11. When 8 more black balls are added to the box, the probability of picking a black ball becomes 5/13. Find the number of white balls in the box. Correct Answer 32

GIVEN :

Probability of picking a black ball is 3/11.

After adding 8 balls , Probability of picking a black ball becomes 5/13.

 

CONCEPT :

Probability

 

ASSUMPTION :

Let the initial no. of black balls in box be ‘x’ and the no. of white balls in box be ‘y’

 

CALCULATION :

Probability of picking a black ball = x/(x + y)

⇒ x/(x + y) = 3/11

⇒ 11x = 3x + 3y

⇒ 8x = 3y      ----(1)

When 8 more black balls are added,

No. of black balls = x + 8

Probability of picking a black ball = (x + 8)/(x + 8 + y)

⇒ (x + 8)/(x + 8 + y) = 5/13

⇒ 13x + 104 = 5x + 40 + 5y

⇒ 8x + 64 = 5y

Substituting from (1),

⇒ 3y + 64 = 5y

⇒ 2y = 64

⇒ y = 64/2 = 32

∴ No. of white balls in box = 32

 

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