Solving problem N4253 Bayesian probability theory

Solving problem N4253 Bayesian probability theory

4253. In two identical boxes are the "Designer" pencils. It is known that one third of the pencils in the first box and 1/4 in the second have TM hardness. A box is selected at random, one pencil is drawn from it at random. It turns out to be hardness tm. What is the likelihood that it is removed from the first box?

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

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