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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

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 Correct Answer b) → a) → d) → c)

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)

Related Questions

Which of the following statements are true?
1. The classical approach to probability theory requires that the total number of possible outcomes be known or calculated and that each of the outcomes be equally likely.
2. A marginal probability is also known as unconditional probability.
3. For three independent events, the joint probability of the three events, P (ABC) = P (A) × P (B/A) × P (C/AB)
4. Two events are mutually exclusive, exhaustive and equally likely, the probability of either event A or B or both occurring P(A or B) = P(A) + P(B)
The following are the two statements relating to the theory of probability. Indicate the statements being correct or incorrect.
Statement I The probability of the joint occurrence of independent events A and B is equal to the probability of event A multiplied by the probability of event B or vice-versa.
Statement II The probability of the joint occurrence of independent event A and dependent event B is equal to the probability of event A multiplied by the conditionalprobability of event B when event A has occurredor vice-versa.
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