Drawing/Picking/Choosing Single/One ball which is neither red nor blue from a bag/urn/box
Problem 4
39 
55 
8 
11 
24 
55 
Solution
Total number of balls in the bag
= 16 Red + 24 White + 15 Blue
= 55
Experiment :
Drawing a ball at random from the bag containing 16 red, 24 white and 15 blue balls
Total Number of Possible Choices
= Number of ways in which one ball can be drawn from the total 55
⇒ n  =  ^{55}C_{1}  
= 
 
=  55 
Let
A : the event of the ball drawn being not red
B : the event of the ball drawn being red or white
C : the event of the ball drawn being neither red nor blue
For Event A
Favorable (White + Blue)  Unfavorable (Red)  Total  

Available  39  16  55 
To Choose  1  0  1 
Choices  ^{39}C_{1}  ^{16}C_{0}  ^{55}C_{1} 
Number of Favorable Choices
= Number of ways in which a ball which is not red can be drawn from the total 39
⇒ m_{A}  =  ^{39}C_{1}  
= 
 
=  39 
Probability of the ball drawn being not red
⇒ Probability of occurrence of Event A
= 

⇒ P(A)  = 
 
= 

Odds
= Total Number of possible choices − Number of Favorable choices
⇒ m_{A}^{c}  =  n − m_{A} 
=  55 − 39  
=  16 
in favor
Odds in Favor of the ball drawn being not red⇒ Odds in Favor of Event A
= Number of Favorable Choices : Number of Unfavorable Choices
= m_{A} : m_{Ac}
= 39 : 16
against
Odds against the ball drawn being not red⇒ Odds against Event A
= Number of Unfavorable Choices : Number of Favorable Choices
= m_{Ac} : m_{A}
= 16 : 39
For Event B
Favorable (Red+ White)  Unfavorable (Blue)  Total  

Available  40  15  55 
To Choose  1  0  1 
Choices  ^{40}C_{1}  ^{15}C_{0}  ^{55}C_{1} 
Number of Favorable Choices
= Number of ways in which a ball which is red or white can be drawn from the total 40
⇒ m_{B}  =  ^{40}C_{1}  
= 
 
=  40 
Probability of the ball drawn being red or white
⇒ Probability of occurrence of Event B
= 

⇒ P(B)  = 
 
= 
 
= 

For Event C
⇒ the ball drawn is white
Favorable (White)  Unfavorable (Red + Blue)  Total  

Available  24  31  55 
To Choose  1  0  1 
Choices  ^{24}C_{1}  ^{31}C_{0}  ^{55}C_{1} 
Number of Favorable Choices
= Number of ways in which a ball which is neither red nor blue can be drawn from the total 24
⇒ m_{C}  =  ^{24}C_{1}  
= 
 
=  24 
Probability of the ball drawn being neither red nor blue
⇒ Probability of occurrence of Event C
= 

⇒ P(C)  = 
 
= 
