A bag contains 3 red balls and 5 black balls. A ball is draw at random from the bag.

Solution:

GIVEN: A bag contains 3 red and 5 black balls and a ball is drawn at random from the bag

TO FIND: Probability of getting a

(i) red ball

(ii) not red ball

Total number of balls 

(i) Total number red balls are 3

We know that PROBABILITY = 

Hence probability of getting red ball is 

(ii) Probability of getting red ball 

We know that sum of probability of occurrence of an event and probability of non occurrence of an event is 1.

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

$\frac{3}{8}+P(\bar{E})=1$

$P(\bar{E})=1-\frac{3}{8}$

$P(\bar{E})=\frac{8-3}{8}=\frac{5}{8}$

Hence the probability of getting not red ball $P(\bar{E})=\frac{5}{8}$