Solving problem N3996 Bayesian probability theory

Solving problem N3996 Bayesian probability theory

3996. The stock of the television studio 45% kinescopes manufactured by plant number 1, 35% - plant number 2, 20% - plant number 3. The probability that the kinescope will not fail during the warranty period is 0.95 for plant 1, 0.98 for plant 2, 0.88 for plant 3. What is the likelihood that it was manufactured by plant number 2, if the kinescope taken at random withstood the warranty period of service?

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