Let A, A2,., A, be n mutually exclusive and exhaustive events de- fined on a sample space S and let H be an arbitrary event defined on S such that P(H)+0, then P(A, |H)= P(HIA,)P(A,) P(HIA)P(A)+P(H/A,)P(A,)+...P(H|A„)P(A,) ·

MATLAB: An Introduction with Applications
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Chapter1: Starting With Matlab
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Prove the theorem

Let 41, A2,., An be n mutually exclusive and exhaustive events de-
fined on a sample space S and let H be an arbitrary event defined on S
such that P(H)÷0, then
P(A, |H)=
P(H/A,)P(A,)
P(H/A,)P(A,)+P(H/A,)P(A,)+...P(H/A„)P(A,)
%3D
Transcribed Image Text:Let 41, A2,., An be n mutually exclusive and exhaustive events de- fined on a sample space S and let H be an arbitrary event defined on S such that P(H)÷0, then P(A, |H)= P(H/A,)P(A,) P(H/A,)P(A,)+P(H/A,)P(A,)+...P(H/A„)P(A,) %3D
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