Probability (Baye’s Theorem)- Previous Years Board Questions (2000 to Sem 2- 2022) with Solutions – ISC – Class 12- Mathematics
BAYE’S THEOREM
Let S be the sample space and 
be n mutually exclusive and exhaustive events associated with a random experiment. If A is any event which occurs with 
then
=\frac{P(A\bigcap&space;E_{i})}{P(A\bigcap&space;E_{1})+P(A\bigcap&space;E_{2})+\,&space;....\,&space;+P(A\bigcap&space;E_{n})})
=\frac{P(E_{i})\,&space;\,&space;P(A/E_{i})}{P(E_{1})P(A/E_{1})+P(E_{2})P(A/E_{2})+\,&space;...\,&space;+P(E_{n})P(A/E_{n})})
Procedure :
(i) First identify mutually exclusive and exhaustive events 
(ii) Then find ,\,&space;P(E_{2}),\,&space;...,\,&space;P(E_{n}))
and check whether the sum of these probabilities is 1.
(iii) Identify the event A and find ,\,&space;P(A/E_{2}),\,&space;....,\,&space;P(A/E_{n}).)
(iv) Calculate )
by using Baye’s Theorem.
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