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 | = | 55C1 | ||
= |
| |||
= | 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 | 39C1 | 16C0 | 55C1 |
Number of Favorable Choices
= Number of ways in which a ball which is not red can be drawn from the total 39
⇒ mA | = | 39C1 | ||
= |
| |||
= | 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
⇒ mAc | = | n − mA |
= | 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
= mA : mAc
= 39 : 16
against
Odds against the ball drawn being not red⇒ Odds against Event A
= Number of Unfavorable Choices : Number of Favorable Choices
= mAc : mA
= 16 : 39
For Event B
Favorable (Red+ White) | Unfavorable (Blue) | Total | |
---|---|---|---|
Available | 40 | 15 | 55 |
To Choose | 1 | 0 | 1 |
Choices | 40C1 | 15C0 | 55C1 |
Number of Favorable Choices
= Number of ways in which a ball which is red or white can be drawn from the total 40
⇒ mB | = | 40C1 | ||
= |
| |||
= | 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 | 24C1 | 31C0 | 55C1 |
Number of Favorable Choices
= Number of ways in which a ball which is neither red nor blue can be drawn from the total 24
⇒ mC | = | 24C1 | ||
= |
| |||
= | 24 |
Probability of the ball drawn being neither red nor blue
⇒ Probability of occurrence of Event C
= |
|
⇒ P(C) | = |
| ||
= |
|