Bayes: did it rain?

It rains 10% of days. A forecaster is correct 80% of the time (on both rainy and dry days). The forecaster predicts rain. What's the probability it actually rains? Pick the closest.

Show hints (2)+
  1. Use Bayes' theorem.
  2. The 10% base rate matters a lot.

Answer

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~31%

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Asked at: Citadel, Two Sigma

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