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'.

Example

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

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

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.

Example

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

   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

   A : the event of getting an even number

   • 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 you get an even number are favourable/favorable to event 'A'. ]

   P : the event of getting a number greater than 4

   • For Event "P"

   Number of favorable/favourable Choices (Or) Number of Successes	=	2 {FIVE, SIX}
   ⇒ mP	=	3

   [All elementary events of the experiment where you get a number greater than 4 are favourable/favorable to event 'P'. ]

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

Of the total possible choices of the experiment (n),

• None or Some (m) are favorable to the occurrence of an event and
• The others are not favourable to the occurrence of the event.

  It is represented as 'n - m' (Or) m^c

This number is a complimentary of the number of favourable choices.

It is the difference between the total number of possible choices and the number of favorable choices in the experiment.

⇒ No. of Unfavourable Choices (Or) Number of Failures	=	Total No. of possible choices − No. of Favourable choices (successes).
⇒ mAc	=	n - mA

⇒ Total No. of possible choices	=	No. of Favourable choices + No. of Unfavourable Choices (Or) [Number of Successes + Number of Failures]
⇒ n	=	mA + mAc

Example

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

   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 Failures	=	1 {TAIL}
   ⇒ mV	=	1

   [All elementary events of the experiment where we get a "TAIL" are favorable to event 'V'. ]

   No. of Unfavourable Choices	=	Total No. of possible choices − No. of Favourable choices (Successes).
   ⇒ mVc	=	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

   M : the event of getting an even number

   • 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 you do not get an even number i.e. where you get an odd number are unfavourable/unfavorable to event 'M'. ]

   • For Event "M" [Alternative]

   Number of favorable/favourable Choices (Or) Number of Failures	=	3 {TWO, FOUR, SIX}
   ⇒ mM	=	3

   [All elementary events of the experiment where you get an even number are favourable/favorable to event 'A'. ]

   No. of Unfavourable Choices (Or) Number of Failures	=	Total No. of possible choices − No. of Favourable choices. (Successes)
   ⇒ mMc	=	n - mM
   	=	6 − 3
   	=	3

   P : the event of getting a number greater than 4

   • 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 you 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 you get a number greater than 4 are favourable/favorable to event 'P'. ]

   No. of Unfavourable Choices	=	Total No. of possible choices − No. of Favourable choices.
   ⇒ mPc	=	n - mP
   	=	6 − 2
   	=	4