Question

A bag contains 15 white and some black balls. if the probability ofdrawing a black ball from the bag is thrice that of drawing a white ball,find the number of black balls in the bag.

Answer 1

Here,
No. of white balls = 15
Let, the no. of black balls be 'x'
Then, total no. of balls = 15 + x
Now,
          P(drawing a white ball) = 15/(15 + x)
And,  P(drawing a black ball) = x/(15 + x)
But A/Q,
               x/(15 + x) = 3*15/(15 + x)
          => x  = 3*15
          => x  = 45
Therefore, there are 45 black balls in the bag.

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Answer 2

Let the no. of black balls in the bag be y

And the bag already contain 15 white balls .

Total no. of balls in bag :- 15 + y

P ( White ball ) :- 15 / ( 15 + y )

P ( Black ball ) :- y / ( 15 + y )

According to the question ,

P ( Black ball ) = 3 [ P ( white ball ) ]


$\frac{y}{15 + y} = 3 \times ( \frac{15}{15 + y} )$

$\frac{y}{15 + y} = \frac{45}{15 + y}$


15y + y² = 675 + 45y

y² + 15y - 45y - 675 = 0

y ( y + 15 ) - 45 ( y + 15 ) = 0

( y + 15 ) ( y - 45 ) = 0


• ( y + 15 ) = 0

y = - 15 ( neglected coz the probability can't be in negative term )

• ( y - 45 ) = 0

y = 45


So, the no. of black balls are 45