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

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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 14C110C024C1

    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 6C19C015C1

    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 26C134C060C1

    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
Author : The Edifier
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