Probability Theory - Lecture 1: Random Experiment , Outcome and Sample Space

What is a Random Experiment?

a random experiment is a process by which we observe something uncertain. After conducting the experiment, the result of the experiment is known.

For example,

◦Rolling a die : Before rolling a die you do not know the result.

◦Tossing a coin: You don’t whether its head or tail before tossing it.

◦Observing the number of goals in a soccer match : we can’t tell total number of goals before the final whistle.

◦Weather : Though it is predictable sometimes, still we can’t be 100% sure. Even in winter we may get a rainy day.

Outcome of a Random Experiment:

The term “Outcome” is a bit technical term. It means the result of the Random Experiment. For every random experiment there are more than one possible outcome and before conducting the experiment we can not say exactly which outcome or result we are going to get. That’s why we call the experiment is a random experiment.

For example, we are tossing an usual coin. Tossing a coin is a random experiment and we will get head or tail as the result or outcome of the random experiment.

We can not say that we will have head before tossing the coin, certainly. Before conducting the random experiment the outcome is uncertain.

Question: Suppose a random experiment has single outcome. Is it wise to call that experiment a random experiment?

For example, suppose you are tossing a coin and the coin has same symbol on both side. Is this tossing experiment a random experiment?

Sample Space:

So far, it is clear to us that, for any random experiment we must have more than one possible outcome.

Sample Space is the set containing the collection of all possible outcomes of the Random experiment.

For example, if we are throwing a die then the sample space is {1,2,3,4,5,6}. If we are tossing a coin then the sample space is {head, tail}.

Question: Suppose we are observing a soccer match of EURO 2020, and counting the total goal scored by both teams. What is the sample space?