The law of total probability can be defined as marginal probability to conditional probability. Total probability elaborates the outcomes of the distinct several events [1]. Total probability law can be used when there is no clear information regarding the probability of events [2].  

1.      Bayesian/ Bayes Theorem

The Bayesian/ Bayes theorem refers to the statistical technique through which conditional/ unconditional probability of the event B can be found if the probability of the A is given and vice versa [3]. The Bayes theorem can support in revising an existing prediction by the given evidence. 

2.      Unconditional and conditional probability

Unconditional and conditional probability are two different types of the probability. Conditional probability provide information about the occurrence of an event on the basis of the previous outcomes and events [4]. The unconditional probability is concerned with the independent chance of the single outcomes results. It elaborates that events are independent and therefor outcomes of the independent events take place independently.

3.      Joint Probability

Joint probability elaborates the likelihood for the situation of two events that occurs relatively at the same time. In other words joint probability elaborates that event A and event B are occurring simultaneously [5].  

4.      Additional rule

The additional rule of the statistics elaborates the concept of addition/ sum in the two different events. According to this rule we calculate the probability by adding up the probability of the event G and event F. Additional rule  shows that events are mutually exclusive even the events are not occurring simultaneously [6].

5.      Multiplication rule

Multiplication rule is very important rule in the statistics. The concept of multiplication rule is related to the two events occurring independently [7]. In this rule probabilities of the two events can be simply multiplied. For instance, multiplying the probability of the event G with the probability of the event F.  The P (G) P(F|G) = P (G ∩ F).

6.      Independent and dependent probability

Independent probability means the outcomes of an event is not influenced by the outcome of the other event. While dependent probability refers to the outcome that is influenced by the outcomes of another event. For instance, if the event A is changing the probability of the event B we will consider it as dependent probability [8]. The outcomes of the both dependent and independent probability cannot be same for an event.  

7.      Axion of Probability  

Axion Probability provide information about the outcome of the event as mathematically self-evident. The probability of an event can be between 0 - 1. The axiom one refers that probability is not negative (in case of 0 outcome), the axiom 2 refers P=1, and the third axiom provide information regarding the mutually exclusive events [9].  

References of Statistics