Lewis Carroll’s fuzzy counters

This site is mostly in Finnish, but I would like to get wider feedback on one posting. I suspect that I am wrong, but have not been able to prove it so far. The Finnish version is here.

A local book publisher, Terra Cognita, publishes weekly classic puzzles.  Last week’s problem has stuck in my mind. It is the fifth puzzle in  Lewis Carroll’s Pillow Problems. It is framed in this way“A bag contains a counter, known to be either white or black. A white counter is put in, the bag is shaken, and a counter is drawn out, which proves to be white. What is now the chance of drawing a white counter?”

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