A bag contains 3 white, 5 black and 2 red balls, all of the same size. A ball is drawn from the bag without looking into it, find the probability that the ball drawn is :

(i) a black ball

(ii) a red ball

(iii) a white ball

(iv) not a red ball

(v) not a black ball

(i) Total number of possible outcomes = Total number of balls = 3 white balls + 5 black balls + 2 red balls = 10

Number of favourable outcomes (Getting a black ball) = 5

P(Getting a black ball) = $\dfrac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$

= $\dfrac{5}{10}$

= $\dfrac{1}{2}$

Hence, the probability of getting a black ball is $\dfrac{1}{2}$.

(ii) Total number of possible outcomes = Total number of balls = 3 white balls + 5 black balls + 2 red balls = 10

Number of favourable outcomes (Getting a red ball) = 2

P(Getting a red ball) = $\dfrac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$

= $\dfrac{2}{10}$

= $\dfrac{1}{5}$

Hence, the probability of getting a red ball is $\dfrac{1}{5}$.

(iii) Total number of possible outcomes = Total number of balls = 3 white balls + 5 black balls + 2 red balls = 10

Number of favourable outcomes (Getting a white ball) = 3

P(Getting a white ball) = $\dfrac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$

= $\dfrac{3}{10}$

Hence, the probability of getting a white ball is $\dfrac{3}{10}$.

(iv) Total number of possible outcomes = Total number of balls = 3 white balls + 5 black balls + 2 red balls = 10

Number of favourable outcomes (Getting not a red ball) = Number of white balls + Number of black balls = 3 + 5 = 8

P(Getting not a red ball) = $\dfrac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$

= $\dfrac{8}{10}$

= $\dfrac{4}{5}$

Hence, the probability of getting not a red ball is $\dfrac{4}{5}$.

(v) Total number of possible outcomes = Total number of balls = 3 white balls + 5 black balls + 2 red balls = 10

Number of favourable outcomes (Getting not a black ball) = Number of white balls + Number of red balls = 3 + 2 = 5

P(Getting not a black ball) = $\dfrac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$

= $\dfrac{5}{10}$

= $\dfrac{1}{2}$

Hence, the probability of getting not a black ball is $\dfrac{1}{2}$.