Event and outcome
An Outcome is a result of a random experiment. For example, when we roll a dice getting six is an outcome.
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.
To know more about Types of Events, visit here.
Experimental probability can be applied to any event associated with an experiment that is repeated a large number of times.
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
To know more about Experimental Probability, visit here.
Theoretical Probability, P(E) = Number of Outcomes Favourable to E / Number of all possible outcomes of the experiment
Here we assume that the outcomes of the experiment are equally likely.
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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
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.
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 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.
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 E¯, representing ‘not E‘, is called the complement of the event E.