A bag contains white, black and red balls only. A ball is drawn at random from the bag. If the probability of getting a white ball is $\dfrac{3}{10}$ and that of a black ball is $\dfrac{2}{5}$, then find the probability of getting a red ball. If the bag contains 20 black balls, then find the number of balls in the bag.

Let probability of getting red ball be x.

We know that,

Probability of getting white, red and black balls are complementary events.

∴ Probability of getting white ball + Probability of getting red ball + Probability of getting black ball = 1

$\Rightarrow \dfrac{3}{10} + x + \dfrac{2}{5} = 1 \\[1em] \Rightarrow x + \dfrac{3 + 4}{10} = 1 \\[1em] \Rightarrow x + \dfrac{7}{10} = 1 \\[1em] \Rightarrow x = 1 - \dfrac{7}{10} \\[1em] \Rightarrow x = \dfrac{3}{10}.$

Given,

Probability of getting black ball = $\dfrac{2}{5}$

$\therefore \dfrac{\text{No. of black balls}}{\text{No. of total balls}} = \dfrac{2}{5} \\[1em] \Rightarrow \dfrac{20}{\text{No. of total balls}} = \dfrac{2}{5} \\[1em] \Rightarrow \text{No. of total balls} = \dfrac{20 \times 5}{2} = 50.$

Hence, probability of drawing red ball = $\dfrac{3}{10}$ and total balls = 50.