Probability

Bayes' Theorem


  • Law of Total Probability:
  • Let S be the sample space and let E1, E2, E3, ....... En are the n-mutually exclusive and exhaustive events associated with the random experiment. Let A be simple event associated with one of these elementary events. Then \tt P(A) = P(E_{1})P(A(E_{1})) + P(E_{2})P(A(E_{2})) + ....... + P(E_{n})P(A(E_{n}))
  • Baye's Theorem
  • Let S be the sample space and let E1, E2, E3 ..... En are the n-mutually exclusive and exhaustive events associated with the random experiment. Let A be the simple event associated with one of these elementary events. Then
    \tt P(E_{K}/A) = \frac{P(A/E_{K})P(E_{K})}{P(E_{1})P(A/E_{1}) + P(E_{2})P(A/E_{2}) + ..... P(E_{K})P(A/E_{K}) + ...... + P(E_{n})P(A/E_{n})}

View the Topic in this video From 15:06 To 43:30

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1. If A is any event which occurs with E1 or E2 or ..... or En, then P(A) = P(E1) P(A / E1) + P(E2) P(A / E2) + .... + P(En) P(A / En)

                                                                    =\sum_{r=1}^n P(Er)P(A / Er) 

2. If A is any event which occurs with E1 or E2 or ..... or En, then probability of occurrence of Ei, when A occurred,

P(E_{i} / A)=\frac{P(E_{i})P(A/E_{i})}{\sum_{i=1}^{n} P(E_{i})P(A/E_{i})}, i = 1, 2, ... , n