Introduction : Probability

Event –

An Event is a set of outcomes. For example when we roll dice the probability of getting a number less than five is an event.Note: An Event can have a single outcome.

Outcome –

An Outcome is a result of a random experiment. For example, when we roll a dice getting six is an outcome.

Experimental probability-

Experimental probability can be applied to any event associated with an experiment that is repeated a large number of times.

Empirical probability –

A trial is when the experiment is performed once. It is also known as empirical probability.

Experimental or empirical probability: P(E) =Number of trials where the event occurred/Total Number of Trials

Theoretical probability-

Here we assume that the outcomes of the experiment are equally likely.
P(E) = Number of Outcomes Favourable to E / Number of all possible outcomes of the      experiment

Elementary event –

An event having only one outcome of the experiment is called an elementary event. Example: Take the experiment of tossing a coin n number of times. One trial of this experiment has two possible outcomes: Heads(H) or Tails(T). So for an individual toss, it has only one outcome, i.e Heads or Tails.

Sum of probabilities-

The sum of the probabilities of all the elementary events of an experiment is one.
Example: take the coin-tossing experiment. P(Heads) + P(Tails )
(1/2)+ (1/2) =1

Impossible event-

An event that has no chance of occurring is called an Impossible event, i.e. P(E) = 0.E.g: Probability of getting a 7 on a roll of a die is 0. As 7 can never be an outcome of this trial.

Sure event-

An event that has a 100% probability of occurrence is called a sure event. The probability of occurrence of a sure event is one.E.g: What is the probability that a number obtained after throwing a die is less than 7?
So,  P(E) = P(Getting a number less than 7) = 6/6= 1

Range of Probability of an event-

The range of probability of an event lies between 0 and 1 inclusive of 0 and 1, i.e. 0≤P(E)≤1.

Geometric probability-

Geometric probability is the calculation of the likelihood that one will hit a particular area of a figure. It is calculated by dividing the desired area by the total area. In the case of Geometrical probability, there are infinite outcomes.

Complimentary events-

Complementary events are two outcomes of an event that are the only two possible outcomes. This is like flipping a coin and getting heads or tails. P(E)+P(¯E)=1, where E and ¯E are complementary events. The event , representing ‘not E‘, is called the complement of the event E.