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

By Experiment or Trial in the subject of probability, we mean a Random experiment unless otherwise specified.

Each trial results in one or more outcomes

Example:

1. Tossing 4 coins
2. Picking 3 balls from a bag containing 10 balls 4 of which are red and 6 blue
3. Rolling a die

Both trial and experiment mean something that is done in anticipation of a result.

However, we sometimes use the two terms together attributing a slightly different sense to the two terms.

Where you are required to differentiate between a trial and an experiment, consider the experiment to be a larger entity formed by the combination of a number of trials.

Example:

1. In the experiment of tossing 4 coins, we may consider tossing each coin as a trial and therefore say that there are 4 trials in the experiment.
2. In the experiment of picking 3 balls from a bag containing 10 balls 4 of which are red and 6 blue, we can consider picking each ball to be an event and therefore say that there are 3 trials in the experiment.

Meaning

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

The results or outcomes or observations of an experiment are called events.

They are generally represented by the capital letters of English Alphabets.

Though we know the possible outcomes of a random experiment, we cannot predict which of these will occur/happen in a conduct of the experiment/trial.

Examples:

1. In the experiment of "Tossing a Coin"
   1. There are two possible Events or Outcomes:
      1. Event "A" : The Event of getting a head
      2. Event "B" : The Event of getting a tail
2. In the experiment of throwing a die
   1. There are six possible Events or Outcomes:
      1. Event "A" : The Event of the die showing up 1 on its face
      2. Event "B" : The Event of the die showing up 2 on its face
      3. ...
      4. Event "E" : The Event of the die showing up 5 on its face
      5. Event "F" : The Event of the die showing up 6 on its face
   2. There are two possible Events or Outcomes [If we view the Event or Outcome in different sense]
      1. Event "M" : The Event of the die showing up an even number on its face
      2. Event "N" : The Event of the die showing up an odd number on its face
   3. There are three possible Events or Outcomes [If we view the Event or Outcome in another sense]
      1. Event "P" : The Event of the die showing up a number divisible by 2
      2. Event "Q" : The Event of the die showing up 1
      3. Event "R" : The Event of the die showing up a non even prime number i.e. 3 or 5

The same experiment can be interpreted in a number of different ways to define different types of events within the experiment.

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

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. Event "A" : The Event of the die showing up 1 on its face
   2. Event "B" : The Event of the die showing up 2 on its face
   3. ...
   4. Event "E" : The Event of the die showing up 5 on its face
   5. Event "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. Event "M" : The Event of the die showing up an even number on its face
   2. Event "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. Event "P" : The Event of the die showing up a number divisible by 2
   2. Event "Q" : The Event of the die showing up 1
   3. Event "R" : The Event of the die showing up a non even prime number i.e. 3 or 5