A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is

(i) red?

(ii) not red?

(i) No. of red balls = 3
    No. of black balls = 5.

Total no. of balls = 3 + 5 = 8.

Let E₁ be the event of drawing a red ball, then number of favourable outcomes to E₁ = 3

$P(E$1) = \dfrac{\text{No. of favourable outcomes to } E1}{\text{Total no. of possible outcomes}} = \dfrac{3}{8}.

Hence, the probability of drawing out a red ball is $\dfrac{3}{8}$.

(ii) Since, there are only two coloured balls red and black. Hence, the probability of not drawing a red ball = probability of drawing a black ball.

Let E₂ be the event of drawing a black ball, then number of favourable outcomes to E₂ = 5

$P(E$2) = \dfrac{\text{No. of favourable outcomes to } E2}{\text{Total no. of possible outcomes}} = \dfrac{5}{8}.

Hence, the probability of drawing out a not red ball is $\dfrac{5}{8}$.