Conditional Probability

The notion of conditional probability states that the happening of one event depends on the occurrence of the other event. The aspect of conditional probability is used to measure and monitor the probability of an event by predicting the occurrence of the other event. The concept of conditional probability could be described as an important statistical tool. The presence of two events is necessary to evaluate the experiment as conditional probability. The scenario of conditional probability comes into play when the occurrence of one event depends on the occurrence of another event. The aspect of dependency is necessary for the prospects of conditional probability.

What is conditional probability?

The aspect of condition probability states that when the occurrence of one event depends on the occurrence of the other event then that experiment is said to be the conditional probability. When the probability of the occurrence of an event happens based on the occurrence of the previous event then it is said to be known as conditional probability. The notion of conditional probability comes into play when there is the presence of a condition. The possible outcome of the previous event is necessary to conduct the process of conditional probability. The calculation of the conditional probability depends on the resulting outcome of the preceding event. The concept of conditional probability does not state a causal relationship between the two possible events. The notion of conditional probability does not indicate that both events must occur at the same time. The aspect of conditions probability could be categorized into two segments namely conditional probability for independent events and conditional probability for mutually exclusive events. 

Formula and examples of conditional probability

The formula of conditional probability is totally based on the theorem of Bayes’. The implementation of conditional probability by using Bayes’ theorem could be described as one of the most influential statistical tools. The formula of conditional probability has been stated as under:

P(A/B) = P(A intersection B)/P(B)

P(A/B)  denotes the aspect of conditional probability

P(A intersection B) denotes the combined probability of event A and event B

P(B) denotes the possibility of the event B

The example of conditional probability states that the occurrence of event A is possible when the occurrence of event B has already taken place. The occurrence of two events is necessary to evaluate the condition of conditional probability. This could be analysed with the help of two events when the occurrence of one event depends on the occurrence of the other event. This could be analyzed with the example of rolling a die. When a die is rolled the number of possible outcomes becomes six. The occurrence of the number of favourable outcomes depends on the nature of the event. The number of possible common outcomes is necessary for the evaluation of the result of conditional probability. The nature of the events must be mutually dependent in order to provide the output of conditional probability. 

Difference between conditional and unconditional probability

The implementation of conditional probability is used in different fields. There are many differences between the conditional and unconditional aspects of probability. The point of difference between the two types of probability is that the result of conditional probability depends majorly on the outcome of the previous event. On the other hand, in the case of unconditional probability, the outcome of the previous event is not necessary to evaluate the occurrence of the present event. In the case of conditional probability, the occurrence of the other event affects one event. In the case of unconditional probability, the occurrence of the other event does not affect the occurrence of one event. The aspect of conditional probability comes with a condition whereas the aspect of unconditional probability comes without any condition. 

Implementation of conditional probability 

The notion of conditional probability could be used in various segments. The concept of conditional probability is widely used in areas like calculus and insurance. The most basic example of conditional probability is the process of re-election in the political parties. The process of re-election depends on the voting preference of the candidates. This example shows the implementation of conditional probability in real-life scenarios. The possible outcome of the conditional probability largely depends on the eventuality of the previous event. This is seen to be highly beneficial in maintaining the equations throughout any projects. The condition of the possible outcome is totally based on the eventuality of the previous event. The implementation of conditional probability could be used in the real-life scenario with the help of Bayes’ theorem, which is described as the most influential statistical technique.

Conclusion

This assignment could be concluded by stating that the segment of conditional probability is applicable in various real-life problems. The different aspects of conditional probability have been evaluated in this assignment. The difference between conditional and unconditional probability has been highlighted in detail. The concept of conditional probability clearly states that the occurrence of a previous event highly affects the occurrence of the present event. The formula of conditional probability has been provided to gather in-depth knowledge regarding the subject matter of the aspects of conditional probability. The notion of conditional probability is totally different from unconditional probability and provides differential results in the conclusion.