Solving problem N3998 Bayesian probability theory

Solving problem N3998 Bayesian probability theory

3998. Of the 30 kinescopes available in a television studio, 7 are produced by plant number 1, 15 by plant number 2, 8 by plant number 3. The probability that the kinescope manufactured by factory No. 1, during the warranty period will not fail, is 0.92. For the kinescope of plant number 2, this probability is 0.93, and for plant number 3 it is 0.85. Selected at random kinescope withdrew the warranty period. Find the probability that it was a kinescope manufactured by the factory №1.

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