Solving problem N3991 Bayesian probability theory

Solving problem N3991 Bayesian probability theory

3991. At the television factory, 40% of TV sets are equipped with imported kinescopes, and 60% of them are domestic. The probability that the TV with an imported kinescope will not fail due to the failure of the kinescope during the warranty period is 0.98, and the similar probability for TVs with a domestic kinescope is 0.82. The purchased TV did not fail due to the failure of the kinescope during the warranty period. What is the likelihood that it was a TV with an imported kinescope?

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