# A bag contains 5 black, 7red and 3 white balls.

Question:

A bag contains 5 black, 7red and 3 white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is :

(i) red

(ii) black or white

(iii) not black

Solution:

GIVEN: A bag contains 7 red, 5 black and 3 white balls and a ball is drawn at random

TO FIND: Probability of getting a

(i) Red ball

(ii) Black or white ball

(iii) Not black ball

Total number of balls

(i) Total number red balls are 7

We know that PROBABILITY =

Hence probability of getting a red ball is equal to

(ii) Total number of black or white balls is

We know that PROBABILITY =

Hence probability of getting white or black ball

(iii) Total number of black balls is 5

We know that PROBABILITY =

Hence probability of getting black ball

We know that sum of probability of occurrence of an event and probability of non

occurrence of an event is 1

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

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

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

$P(\bar{E})=\frac{2}{3}$

Hence the probability of getting non black ball $P(\bar{E})=\frac{2}{3}$