Solving problem N3994 Bayesian probability theory

Solving problem N3994 Bayesian probability theory

3994. 30% of the picture tubes in stock are made at plant number 1, the rest are made at plant number 2. The probability that a kinescope manufactured at plant No. 1 does not fail during the warranty period is 0.9, for kinescopes from plant 2, this probability is 0.8. Randomly, we chose a kinescope for checking from the warehouse, which withstood the warranty period. Determine the probability that it was manufactured at the factory №2.

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