# Trial, Experiment, Event, Result, Outcome, in Probability

## What is a Trial?

Any particular performance of a random experiment is called a trial. Each trial results in one or more outcomes. Experiment/Trial, in the subject of probability, unless otherwise specified, means a Random experiment.

### Examples

1. Tossing 4 coins.
2. Rolling one or more dice.
3. Arranging the letters of a word.
4. Seating 10 children in a row, 6 of whom are boys and the rest girls.
5. Picking 3 balls from a bag containing 10 balls 4 of which are red and 6 blue.

## Trial vs. Experiment

Both trial and experiment mean something that is done in anticipation of a result. Many a times we use the words trial and experiment synonymously.

We sometimes use the two terms together wherein we have to attribute a distinct sense to each of the two terms. In such cases, an experiment is considered a larger entity formed by or involving a number of trails.

### Examples

1. #### Tossing 4 coins

 Experiment Tossing 4 Coins. Tossing each coin.

We can consider the act of tossing each coin as a trial and thus say that there are 4 trials in the experiment of tossing 4 coins.

2. #### Picking 3 balls from a bag containing 10 balls

 Experiment Picking the 3 balls. Picking each ball.

We can consider the act of picking each ball as a trail and thus say that there are 3 trials in the experiment of picking 3 balls from a bag containing 10 balls.

## Event or Outcome

### Event

#### Meaning

1. Something that results.
2. A result that is caused by some previous action.

In Probability, the results or outcomes or observations of an experiment are called events.

### Representing Events

Events are generally represented by the capital letters of English Alphabets.
• "A" : The event of getting a head.
• "M" : The event of throwing an even number on tossing a dice.

It is not a necessity that the alphabets used for naming events are to be considered sequentially. They can be considered in any order. However, taking them in a sequential manner would aid understanding.

### Number of possible Events

The number of possible events in relation to an experiment is dependent on both the experiment as well the definition for the event.

#### Examples

• ##### Tossing a Coin
In the experiment of "Tossing a Coin",

1. if we consider getting a head/or tail as an event,

There are two possible Events or Outcomes:

1. Event "A" : Getting a head.
2. Event "B" : Getting a tail.

• ##### Throwing a Die/Dice
In the experiment of throwing a die,

1. if we consider getting a number on the die/dice as an event,

There are six possible Events or Outcomes:

1. Event "A" : The die showing up 1 on its face.
2. Event "B" : The die showing up 2 on its face.
3. ...
4. Event "E" : The die showing up 5 on its face.
5. Event "F" : The die showing up 6 on its face.

2. if we consider getting an even/odd number on the die/dice as an event,

There are two possible Events or Outcomes

1. Event "M" : The die showing up an even number on its face
2. Event "N" : The die showing up an odd number on its face

3. the events we consider may be any combination of the possible events in the experiment,

There are three possible Events or Outcomes

1. Event "P" : The die showing up a number divisible by 2
2. Event "Q" : The die showing up 1
3. Event "R" : The die showing up a non even prime number i.e. 3 or 5

### Occurrence of Events

We can enumerate all the possible outcomes/results of a random experiment. When the random experiment is conducted, none or more of the possible events would occur. However,it would not be possible to predict with certainty which of the events would occur in a particular conduct of the experiment.

## An Event is what we define it to be

An event is what we define/consider/view it to be. By changing the definitions for the events, the same experiment can be interpreted in a number of different ways.

The number of possible events or outcomes in an experiment are dependent on what we define the event to be.

### Examples

In the experiment of throwing a die
1. If getting a digit is defined as an event, there are six possible events or outcomes.

1. A - The Event of the die showing up 1 on its face.
2. B - The Event of the die showing up 2 on its face.
3. ...
4. E - The Event of the die showing up 5 on its face.
5. F - The Event of the die showing up 6 on its face

2. If getting an even number and getting an odd number are defined to be the events, there are only two possible Events or Outcomes

1. M - The Event of the die showing up an even number on its face.
2. N - The Event of the die showing up an odd number on its face.

3. If getting a number divisible by 2 is an event, getting 1 is another event and getting a non even prime number is another event, then there are three possible Events or Outcomes.

1. P - The Event of the die showing up a number divisible by 2
2. Q - The Event of the die showing up 1
3. R - The Event of the die showing up a non even prime number i.e. 3 or 5

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