For calculating posterior probabilities (conditional probabilities under statistical dependence), the following information is available 

a) conditional probabilities 

b) original probability estimates (prior probabilities) of mutually exclusive and collectively exhaustive events 

c) Arbitrary event with probability # 0 and for which conditional probabilities are also known 

d) Joint probabilities of prior probability and conditional probability 

Given the information that the arbitrary event has occurred, arrange the above information in a sequence of their requirement as per Baye's Theorem 

Choose the correct option: 

Posterior probability

1. A posterior probability, in Bayesian statistics, is the revised or updated probability of an event occurring after taking into consideration new information.
2. The posterior probability is calculated by updating the prior probability using Bayes' theorem.
3. In statistical terms, the posterior probability is the probability of event A occurring given that event B has occurred. 
4.  This theorem is also known as ‘Inverse probability theorem’ because here moving from the first stage to the second stage, we again find the probabilities (revised) of the events of the first stage i.e. we move inversely.
5. Thus, using this theorem, probabilities can be revised on the basis of having some related new information.

We require the following information in order to derive posterior probability:

1. original probability estimates (prior probabilities) of mutually exclusive and collectively exhaustive events 
2. conditional probabilities 
3. Joint probabilities of prior probability and conditional probability 
4. Arbitrary event with probability # 0 and for which conditional probabilities are also known 

Thereafter, we can substitute the values in the formula for deriving posterior probability.

Hence, For calculating posterior probabilities (conditional probabilities under statistical dependence) the correct sequence is b) → a) → d) → c)