# Problem 5

Define the Event and identify the number of favourable choices in the following cases which relate to the experiment of drawing a ball
1. Drawing a ball which is not blue from a box containing 24 balls of the same shape and weight of which 8 are green, 6 are red and the rest are blue.
2. Drawing a ball which is neither a black ball nor a green ball from a bag containing 4 green, 5 black, 6 white balls.
3. Choosing a ball which is either red or blue from a bag containing 18 white, 16 green, 14 blue and 12 red balls.
Ans : i) 14, ii) 6, iii) 26

# Solution

1. Total number of balls in the bag

= 24

Number of blue balls in the bag

= Total number of balls − (number of green balls + number of red balls)

= 24 − (8 + 6)

= 24 − (14)

= 10

Experiment :

Drawing a ball at random from the bag containing 8 green, 6 red and rest blue balls

Let

A : the event of drawing a ball which is not blue

## For Event A

 Favorable (Green + Red) Unfavorable (Blue) Total Available 14 10 24 To Choose 1 0 1 Choices 14C1 10C0 24C1

Number of Favorable Choices

= Number of ways in which a ball which is not blue can be drawn from the total 14

⇒ mA = 14C1
=
 14 1
= 14
2. Total number of balls in the bag

= 4 Green + 5 Black + 6 White

= 15

Experiment :

Drawing a ball at random from the bag containing 4 green, 5 black and 6 white balls

Let

B : the event of drawing a ball which is neither black nor green

## For Event B

 Favorable (White) Unfavorable (Black + Green) Total Available 6 9 15 To Choose 1 0 1 Choices 6C1 9C0 15C1

Number of Favorable Choices

= Number of ways in which a ball which is neither black nor green can be drawn from the total 6

⇒ mB = 6C1
=
 6 1
= 6
3. Total number of balls in the bag

= 18 white + 16 green + 14 blue + 12 red

= 60

Experiment :

Drawing a ball at random from the bag containing 18 white, 16 green, 14 blue and 12 red balls

Let

C : the event of drawing a ball which is either red or blue

## For Event C

 Favorable (Red + Blue) Unfavorable (White + Green) Total Available 26 34 60 To Choose 1 0 1 Choices 26C1 34C0 60C1

Number of Favorable Choices

= Number of ways in which a ball which is either red or blue can be drawn from the total 26

⇒ mC = 26C1
=
 26 1
= 26