A bag contains 5 white and 7 red balls.
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

$P(E)+P(\bar{E})=1$

$\frac{4}{9}+P(\bar{E})=1$

$P(\bar{E})=1-\frac{4}{9}$

$P(\bar{E})=\frac{5}{9}$