Some Basic Terminology used in Probability

Experiment: An experiment is known as an event in which some well-defined outcome is expected.  Also known as sample space. For example, sample space S is S = {H, T}, where H refers to head and T refers to Tail.

Trial: A trial is known as a single event that is performed to determine the outcome.

Outcome: Outcomes are the results of an experiment. For example, win/loss are possible outcomes of the cricket match.

Random experiment: A random experiment is an experiment whose outcome may not be predicted in advance. It may be repeated under numerous conditions. 

Impossible Event: When the probability of an event is 0, then the event is known as an impossible event.

Sure Event: When the probability of an event is 1, then the event is known as a sure event.

Probability Formula

The experimental probability or empirical probability of an event is 

Probability(E) = [Tex]\frac{Total \ number \ of \ favorable \ outcomes}{Total \ number \ of \ all \ possible \ outcomes}[/Tex]

Alternatively,    

P(E) = [Tex]\frac{N(E)}{N(S)}[/Tex]

Here, P(E) = Probability of an event to occur

N(E) = Total number of favorable outcomes

N(S) = Total number of all possible outcomes

Now let’s move on to solving problems and understanding probability better. 

Probability, in simple words, is the prediction of the happening of an event before it has already happened. We do prediction in many things in our day-to-day lives, like:

• Predict the weather before going for a picnic.

• Predict the outcome of the election.

• Predict who is going to win the toss.

In all these situations we try to find the probability or chances of occurring of an event by considering all the conditions which are in favor of that event. From the above discussion probability can be defined mathematically as :

Probability is the branch of mathematics that tells us what are the chances for an event to occur. The probability of an event is a number between 0 and 1, where 0 indicates the impossibility of the event and 1 indicates certainty. Therefore, 0 ≤ P(E) ≤ 1, where P(E) = Probability of an event occurring.