Drawing/Picking/Choosing a red or black ball from a bag/urn/box
Problem 3
A bag contains 3 red balls, 4 white balls and 7 black balls the probability of drawing a red or a black ball is
Ans :
5 
7 
Solution
Total number of balls in the bag
= 3 Red + 4 White + 7 Black
= 14
Experiment :
Drawing a ball at random from the bag containing 3 red, 4 white and 7 black balls
Total Number of Possible Choices
= Number of ways in which one ball can be drawn from the total 14
⇒ n  =  ^{14}C_{1}  
= 
 
=  14 
Let
A : the event of drawing a red or a black ball
For Event A
Favorable (Red + Black)  Unfavorable (Others)  Total  

Available  10  4  14 
To Choose  1  0  1 
Choices  ^{10}C_{1}  ^{4}C_{0}  ^{14}C_{1} 
Number of Favorable Choices
= Number of ways in which one red or black ball can be drawn from the total 10
⇒ m_{A}  =  ^{10}C_{1}  
= 
 
=  10 
Probability of the ball drawn being red or black
⇒ Probability of occurrence of Event A
= 

⇒ P(A)  = 
 
= 
 
= 

Author : The Edifier