Question

A bag contains 3 red balls and 5 black balls. A ball is draw at random from the bag. What is the probability that the ball drawn is  not red? 

Answer 1

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 ${\displaystyle 3+5=8}$

 Probability of getting red ball ${\displaystyle P\left(E\right)=\frac{3}{8}}$

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

${\displaystyle P\left(\overline{E}\right)+P\left(\overline{E}\right)=1}$

${\displaystyle \frac{3}{8}+P\left(\overline{E}\right)=1}$

${\displaystyle P\left(\overline{E}\right)=1-\frac{3}{8}}$

${\displaystyle P\left(\overline{E}\right)=\frac{8-3}{8}=\frac{5}{8}}$

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