Solving problem N3882 Bayesian probability theory

Solving problem N3882 Bayesian probability theory

3882. To signal that the automatic line mode deviates from the normal, an indicator is used. It belongs with probabilities 0,2; 0.3; 0.5 to one of three types for which the probabilities of operation are equal respectively to 1; 0.75; 0.4. From the indicator received a signal. What type of indicator is most likely to belong to?

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Detailed solution. Decorated in Microsoft Word 2003 (Quest decided to use the formula editor)