Favorable/Unfavourable Total/Possible Choices/Cases/Events Successes/Failures - Experiment :: Probability

Possible Choices or Cases or Events or Outcomes

The total number of possible outcomes of an experiment i.e. the number of elementary events possible in an experiment form the number of possible choices or cases in the experiment.

In its most common notation, this is represented by the letter 'n'.

Examples

  1. In the experiment of tossing a coin,

    There are two possible outcomes or elementary events.

    1. The event of getting a HEAD.
    2. The event of getting a TAIL.

    Therefore the total number of possible choices in this experiment is 2 ⇒ n = 2

  2. In the experiment of throwing a die,

    There are six possible outcomes or elementary events.

    1. The event of 1 appearing on the face of the die.
    2. The event of 2 appearing on the face of the die.
    3. ...
    4. ...
    5. ...
    6. The event of 6 appearing on the face of the die.

    Therefore the total number of possible choices in this experiment is 6 ⇒ n = 6

  3. In the experiment of drawing a card from a pack of 52 cards,

    Since any one of the cards may appear, there are 52 possible outcomes or elementary events.

    Therefore the total number of possible choices in this experiment is 52 ⇒ n = 52

  4. In the experiment of drawing a letter from the letters of the word COURAGE,

    Since any one of the 7 letters may be drawn, there are 7 possible outcomes or elementary events.

    Therefore the total number of possible choices in this experiment is 7 ⇒ n = 7

Favourable/Favorable cases/choices/events/outcomes or Successes

The cases or choices or elementary events which ensure the occurrence of an event are called favourable/favorable cases or choices for the event.

Successes for an Event

The number of Favourable/Favorable Choices for an event is also identified as the number of successes for the occurrence of the event.

Representing Number of Successes/Favourable Choices for an Event

In its most common notation, the number of Favourable/Favorable choices or number of successes is represented by the letter 'm', sometimes followed by a subscript (mA, mB etc) to indicate the event for which the choices are favourable/favorable.

Examples

  1. In the experiment of tossing a coin,

    There are two possible results/outcomes i.e. there are two possible elementary events/choices.

    1. The event of getting a HEAD.
    2. The event of getting a TAIL.

    Let

    1. A : The event of getting a tail.

    • For Event A

    Number of favorable/favourable Choices
    (Or) Number of Successes

    =

    1 {TAIL}
    ⇒ mA = 1
    All elementary events of the experiment where we get a "TAIL" are favorable to event 'A'.

  2. In the experiment of throwing a die,

    There are six possible outcomes or elementary events.

    1. The event of 1 appearing on the face of the die.
    2. The event of 2 appearing on the face of the die.
    3. ...
    4. ...
    5. ...
    6. The event of 6 appearing on the face of the die.

    Let

    1. A : The event of getting an even number.
    2. P : The event of getting a number greater than 4.

    • For Event A

    Number of favorable/favourable Choices
    (Or) Number of Successes

    =

    3 {TWO, FOUR, SIX}
    ⇒ mA = 3
    All elementary events of the experiment where we get an even number are favourable/favorable to event 'A'.

    • For Event P

    Number of favorable/favourable Choices
    (Or) Number of Successes

    =

    2 {FIVE, SIX}
    ⇒ mP = 2
    All elementary events of the experiment where we get a number greater than 4 are favourable/favorable to event 'P'.

UnFavourable/UnFavorable cases/choices/events/outcomes or Failures

The cases or choices or elementary events which ensure the non-occurrence of an event are called unfavourable/unfavorable cases or choices for the event.

Failures for an Event

The number of Unfavourable/Unfavorable Choices for an event are also identified as the number of failures for the occurrence of the event.

Representing Number of Successes/Favourable Choices for an Event

Of all the possible choices in relation to an experiment (n),
  • None or some (m) are favorable to the occurrence of an event and
  • The rest are not favourable to the occurrence of the event.

The number of unfavourable/unfavorable choices (failures) is a complimentary of the number of favorable/favourable choices (successes) and is obtained as the difference between the total number of possible choices in the experiment and the number of favourable/favorable choices (successes) for the event.

It is denoted by 'n - m' (Or) mc

Number of unfavorable/unfavourable Choices (Failures)
= Total Number of possible choices
    - Number of Favorable/Favourable choices (successes)
⇒ mA = n - mA

Total Number of possible Choices
= Number of Favorable/Favourable choices
    + Number of Unfavorable/Unfavourable choices
(Or) = Number of Successes + Number of Failures
⇒ n = mA + mAc

Examples

  1. In the experiment of tossing a coin,

    There are two possible results or outcomes i.e. there are two possible elementary events or choices.

    1. The event of getting a HEAD.
    2. The event of getting a TAIL.

    Let

    1. V : The event of getting a tail.

    • For Event V

    Number of unfavorable/unfavourable Choices
    (Or) Number of Failures

    =

    1 {HEAD}
    ⇒ mVc = 1
    All elementary events of the experiment where we get a "HEAD" are unfavorable to event 'V'.

    • For Event V (alternative)

    Number of favorable/favourable Choices
    (Or) Number of Successes

    =

    1 {TAIL}
    ⇒ mV = 1
    All elementary events of the experiment where we get a "TAIL" are favorable to event 'V'.

    Number of unfavorable/unfavourable Choices (Failures)
    = Total Number of possible choices
        - Number of Favorable/Favourable choices (successes)
    ⇒ mV = n - mV
    = 2 - 1
    = 1

  2. In the experiment of throwing a die,

    There are six possible outcomes or elementary events.

    1. The event of 1 appearing on the face of the die.
    2. The event of 2 appearing on the face of the die.
    3. ...
    4. ...
    5. ...
    6. The event of 6 appearing on the face of the die.

    Let

    1. M : The event of getting an even number.
    2. P : The event of getting a number greater than 4.

    • For Event M

    Number of unfavorable/unfavourable Choices
    (Or) Number of Failures

    =

    3 {ONE, THREE, FIVE}
    ⇒ mMc = 3
    All elementary events of the experiment where we do not get an even number i.e. where we get an odd number are unfavourable/unfavorable to event 'M'.

    • For Event M (alternative)

    Number of favorable/favourable Choices
    (Or) Number of Successes

    =

    3 {TWO, FOUR, SIX}
    ⇒ mM = 3
    All elementary events of the experiment where we get an even number are favourable/favorable to event 'M'.

    Number of unfavorable/unfavourable Choices (Failures)
    = Total Number of possible choices
        - Number of Favorable/Favourable choices (successes)
    ⇒ mM = n - mM
    = 6 - 3
    = 3

    • For Event P

    Number of unfavorable/unfavourable Choices
    (Or) Number of Failures

    =

    4 {ONE, TWO, THREE, FOUR}
    ⇒ mPc = 4
    All elementary events of the experiment where we do not get a number greater than 4 are unfavourable/unfavorable to event 'P'.

    • For Event P (alternative)

    Number of favorable/favourable Choices
    (Or) Number of Successes

    =

    2 {FIVE, SIX}
    ⇒ mP = 2
    All elementary events of the experiment where we get a number greater than 4 are favourable/favorable to event 'P'.

    Number of unfavorable/unfavourable Choices (Failures)
    = Total Number of possible choices
        - Number of Favorable/Favourable choices (successes)
    ⇒ mP = n - mP
    = 6 - 2
    = 4

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