$A$ 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?

(A) $(i)$ Total number of balls in the bag $= 3 + 5 = 8$.
The probability of drawing a red ball is given by the formula: $P(\text{red}) = \frac{\text{Number of favourable outcomes}}{\text{Total number of possible outcomes}}$.
$P(\text{red}) = \frac{3}{8}$.
$(ii)$ The probability of not drawing a red ball is the complement of drawing a red ball.
$P(\text{not red}) = 1 - P(\text{red})$.
$P(\text{not red}) = 1 - \frac{3}{8} = \frac{8 - 3}{8} = \frac{5}{8}$.