Question:
A bag contains 5 white and 7 red balls. One ball is drawn at random. What is the probability that ball drawn is not black?
Solution:
GIVEN: A bag contains 6 red, 8 black and 4 white balls and a ball is drawn at random
TO FIND: Probability that the ball drawn is not black
Total number of balls 
Total number of black balls is 8
We know that PROBABILITY = 
Probability of getting a black ball 
We know that sum of probability of occurrence of an event and probability of non occurrence of an event is 1.
Hence
$P(E)+P(\bar{E})=1$
$\frac{4}{9}+P(\bar{E})=1$
$P(\bar{E})=1-\frac{4}{9}$
$P(\bar{E})=\frac{5}{9}$