Question

In a box, there are 10 white balls, 8 red balls and some black balls. If the probability of selecting a black ball is equal to the sum of probabilities of selecting a white ball and a red ball, then the number of black balls in the box is

• A.
  10
• B.
  8
• C.
  18
• D.
  30

Answer 1

The correct option is C

18
There are 10 white balls and 8 red balls.

Let the number of black balls be x.
Therefore, the total number of balls is $18+x.$

$P\left(blackball\right)=\frac{\text{Number of black balls}}{Totalnumberofballs}=\frac{x}{18+x}P\left(whiteball\right)=\frac{\text{Number of white balls}}{Totalnumberofballs}=\frac{10}{18+x}P\left(redball\right)=\frac{\text{Number of red balls}}{Totalnumberofballs}=\frac{8}{18+x}$

Now, it is given that $P\left(blackball\right)=P\left(whiteball\right)+P\left(redball\right).\Rightarrow \frac{x}{18+x}=\frac{10}{18+x}+\frac{8}{18+x}\Rightarrow \frac{x}{18+x}=\frac{10+8}{18+x}\Rightarrow x=18$

Thus, the number of black balls is 18.

Hence, the correct answer is option c.