Solving problem N3992 Bayesian probability theory

Solving problem N3992 Bayesian probability theory

3992. The stock of the television studio has 70% of picture tubes made by plant No. 1, the rest of the picture tubes are made by plant No. 2. The probability that the kinescope will not fail during the warranty period of service is equal to 0.8 for the kinescope of factory No. 1, and 0.7 for the kinescope of factory No. 2. Find the probability that the taken kinescope will withstand the warranty service life. The kinescope survived the warranty period. Find the probability that it is manufactured by plant number 2.

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