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

## 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. ### Examples

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

- In the experiment of
**tossing a coin**,There are two possible outcomes or elementary events.

- The event of getting a HEAD.
- The event of getting a TAIL.

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

**n = 2** - In the experiment of
**throwing a die**,There are six possible outcomes or elementary events.

- The event of 1 appearing on the face of the die.
- The event of 2 appearing on the face of the die.
- ...
- ...
- ...
- 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** - 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** - 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

### Representing Number of Successes/Favourable Choices for an Event

### Examples

The number of Favourable/Favorable Choices for an event is also identified as the number of successes for the occurrence of the 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 (**m**_{A}, m_{B} etc) to indicate the event for which the choices are favourable/favorable.

- In the experiment of
**tossing a coin**,There are two possible results/outcomes i.e. there are two possible elementary events/choices.

- The event of getting a HEAD.
- The event of getting a TAIL.

Let

- A : The event of getting a tail.

#### • For Event

__A__Number of favorable/favourable Choices

(Or) Number of Successes

=

1 {TAIL}⇒ m _{A}= 1 All elementary events of the experiment where we get a "TAIL" are favorable to event 'A'. - In the experiment of
**throwing a die**,There are six possible outcomes or elementary events.

- The event of 1 appearing on the face of the die.
- The event of 2 appearing on the face of the die.
- ...
- ...
- ...
- The event of 6 appearing on the face of the die.

Let

- A : The event of getting an even number.
- 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}⇒ m _{A}= 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}⇒ m _{P}= 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

### Representing Number of Successes/Favourable Choices for an Event

### Examples

The number of Unfavourable/Unfavorable Choices for an event are also identified as the number of failures for the occurrence of the 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) m^{c}

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

= | Total Number of possible choices - Number of Favorable/Favourable choices (successes) | |

⇒ m_{A} | = | n - m_{A} |
---|

Total Number of possible Choices | ||

= | Number of Favorable/Favourable choices + Number of Unfavorable/Unfavourable choices | |

(Or) | = | Number of Successes + Number of Failures |

⇒ n | = | m_{A} + m_{A}^{c} |
---|

- In the experiment of
**tossing a coin**,There are two possible results or outcomes i.e. there are two possible elementary events or choices.

- The event of getting a HEAD.
- The event of getting a TAIL.

Let

- V : The event of getting a tail.

#### • For Event

__V__Number of unfavorable/unfavourable Choices

(Or) Number of Failures

=

1 {HEAD}⇒ m _{V}^{c}= 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}⇒ m _{V}= 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)⇒ m _{V}= n - m _{V}= 2 - 1 = 1 - In the experiment of throwing a die,
There are six possible outcomes or elementary events.

- The event of 1 appearing on the face of the die.
- The event of 2 appearing on the face of the die.
- ...
- ...
- ...
- The event of 6 appearing on the face of the die.

Let

- M : The event of getting an even number.
- 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}⇒ m _{M}^{c}= 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}⇒ m _{M}= 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)⇒ m _{M}= n - m _{M}= 6 - 3 = 3 #### • For Event

__P__Number of unfavorable/unfavourable Choices

(Or) Number of Failures

=

4 {ONE, TWO, THREE, FOUR}⇒ m _{P}^{c}= 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}⇒ m _{P}= 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)⇒ m _{P}= n - m _{P}= 6 - 2 = 4

... 678 ... |

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