Solving problem N4240 Bayesian probability theory

Solving problem N4240 Bayesian probability theory

4240. The assembler received three boxes of parts. In the first box there are 40 parts, of which 20 are of the highest grade, in the second 50 parts, of which 10 are of the highest grade, in the third are 30 parts, of which 12 are of the highest grade. From the randomness of the box taken, a top-grade item was extracted. Determine the likelihood that this part is removed from the 1st drawer.

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