Given that,
A bag contains $3$ red and $5$ black balls.
Therefore, the total no. of possible outcomes $=8$ ($3$ red $+5$ black)
(i)Now Let E = event of getting red ball.
So, No. of favorable outcomes $=3$ (as there are $3$ red)
We know that Probability, P(E) = Number of favorable outcomes/ Total number of outcomes
P(E) $=3/8$
(ii) Let
$(\overset{\scriptscriptstyle\rightharpoonup}{E})$ event of getting no red ball.
Therefore, From the previous question we already have P(E) $=3/8$
$P(\overset{\scriptscriptstyle\rightharpoonup}{E})+P(\overset{\scriptscriptstyle\rightharpoonup}{E})=1$
$P(\overset{\scriptscriptstyle\rightharpoonup}{E})=1-P(E)$
$P(\overset{\scriptscriptstyle\rightharpoonup}{E})=1-\frac{3}{8}$
$P(\overset{\scriptscriptstyle\rightharpoonup}{E})=\frac{5}{8}$