Solving problem N3860 Bayesian probability theory

Solving problem N3860 Bayesian probability theory

3860. The assembler received 4 boxes of parts manufactured by plant No. 1 and 6 boxes of parts manufactured by plant No. 2. The probability that a part of factory number 1 is standard is 0.7, and that of factory number 2 is 0.8. The collector picked up the item at random from the box taken at random. Standard part removed. Determine the probability that it is made by the factory №2.

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