Solving problem N3997 Bayesian probability theory

Solving problem N3997 Bayesian probability theory

3997. Of the 30 kinescopes available in a television studio, 7 are produced by plant number 1, 15 by plant number 2, eight by plant number 3. The probability that the picture tube manufactured by plant number 1 will not fail during the warranty period is 0.95. For a kinescope of plant number 2, this probability is 0.9, and for plant number 3 it is 0.8. Selected at random kinescope withdrew the warranty period. Find the probability that it was a kinescope manufactured by plant number 3.

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