Drawing a Card from a Pack - Define Events and Find number of favorable choises

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Problem 6

Define the Event and identify the number of favourable choices in the following cases which relate to the experiment of drawing a card from a pack of cards:
  1. The card is a king or a queen.
  2. Getting a number card.
  3. red or black
  4. Either a face card (jack, queen, king) or a six.
  5. At least a spade or a king
  6. Getting a queen of a club or king of heart
  7. Either a red or a numbered card
  8. Either black or an ace
  9. Neither a spade nor a heart.
Ans : [8, 40, 52, 16, 16, 2, 46, 28, 26]

Solution

Experiment :

Drawing a card from a pack of 52 cards

(assumed to be a normal set of cards)

  1. Let

    A : the event of the card drawn being a king or a queen.

    For Event A

    Favorable
    (Kings + Queens)     		Unfavorable
    (Others)     		Total
    Available 8 44 52
    To Choose 1 0 1
    Choices 8C144C052C1

    Number of Favorable Choices

    = Number of ways in which one card can be drawn from the total 8 favorable cards

    ⇒ mA = 8C1
    =
    8
    1
    = 8

  2. Let

    B : the event of the card drawn being a numbered card.

    For Event B

    Favorable
    (Numbered Cards)     		Unfavorable
    (Others)     		Total
    Available 40 12 52
    To Choose 1 0 1
    Choices 40C112C052C1

    Number of Favorable Choices

    = Number of ways in which one card can be drawn from the total 40 favorable cards

    ⇒ mB = 40C1
    =
    40
    1
    = 40

  3. Let

    C : the event of the card drawn being a red or black card.

    For Event C

    Favorable
    (Red + Black)     		Unfavorable
    (Others)     		Total
    Available 52 0 52
    To Choose 1 0 1
    Choices 52C10C052C1

    Number of Favorable Choices

    = Number of ways in which one card can be drawn from the total 52 favorable cards

    ⇒ mC = 52C1
    =
    52
    1
    = 52

    This is a certain event whose probability would be 1.

  4. Let

    D : the event of the card drawn being either a face card (king, queen, jack) or a six.

    For Event D

    Favorable
    (Face cards or Sixes)     		Unfavorable
    (Others)     		Total
    Available 16 36 52
    To Choose 1 0 1
    Choices 16C136C052C1

    Number of Favorable Choices

    = Number of ways in which one card can be drawn from the total 16 favorable cards

    ⇒ mD = 16C1
    =
    16
    1
    = 16

  5. Let

    E : the event of getting at least a spade or a king.

    For Event E

    Favorable
    (Spades + Kings)     		Unfavorable
    (Others)     		Total
    Available 16 36 52
    To Choose 1 0 1
    Choices 16C136C052C1

    Number of Favorable Choices

    = Number of ways in which one card can be drawn from the total 16 favorable cards

    ⇒ mE = 16C1
    =
    16
    1
    = 16

  6. Let

    F : the event of the card drawn being a queen of a club or a king of a heart

    For Event F

    Favorable
    (Queen of Club +
    King of Heart)     		Unfavorable
    (Others)     		Total
    Available 2 50 52
    To Choose 1 0 1
    Choices 2C150C052C1

    Number of Favorable Choices

    = Number of ways in which one card can be drawn from the total 2 favorable cards

    ⇒ mF = 2C1
    =
    2
    1
    = 2

  7. Let

    G : the event of getting either a red or a numbered card

    For Event G

    Favorable
    (Red Cards +
    Other Numbered Cards)     		Unfavorable
    (Others)     		Total
    Available 46 6 52
    To Choose 1 0 1
    Choices 46C16C052C1

    Number of Favorable Choices

    = Number of ways in which one card can be drawn from the total 46 favorable cards

    ⇒ mG = 46C1
    =
    46
    1
    = 46

  8. Let

    H : the event of the card drawn being a black or an ace

    For Event H

    Favorable
    (Black Cards + Other Aces)     		Unfavorable
    (Others)     		Total
    Available 28 24 52
    To Choose 1 0 1
    Choices 28C124C052C1

    Number of Favorable Choices

    = Number of ways in which one card can be drawn from the total 28 favorable cards

    ⇒ mH = 28C1
    =
    28
    1
    = 28

  9. Let

    I : the event of the card drawn being neither a spade nor a heart

    For Event I

    Favorable
    (Others)     		Unfavorable
    (Spades + Hearts)     		Total
    Available 26 26 52
    To Choose 1 0 1
    Choices 26C126C052C1

    Number of Favorable Choices

    = Number of ways in which one card can be drawn from the total 26 favorable cards

    ⇒ mI = 26C1
    =
    26
    1
    = 26
Author : The Edifier
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