# Event and Number of favorable choices - Drawing/Picking/Choosing Single/One ball from a bag/urn/box

# Problem 5

- 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.
- Drawing a ball which is neither a black ball nor a green ball from a bag containing 4 green, 5 black, 6 white balls.
- Choosing a ball which is either red or blue from a bag containing 18 white, 16 green, 14 blue and 12 red balls.

# Solution

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 ^{14}C_{1}^{10}C_{0}^{24}C_{1}Number of Favorable Choices

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

⇒ m _{A}= ^{14}C_{1}= 14 1 = 14 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 ^{6}C_{1}^{9}C_{0}^{15}C_{1}Number of Favorable Choices

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

⇒ m _{B}= ^{6}C_{1}= 6 1 = 6 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 ^{26}C_{1}^{34}C_{0}^{60}C_{1}Number of Favorable Choices

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

⇒ m _{C}= ^{26}C_{1}= 26 1 = 26