Imagine there are two urns — urn A and urn B. Urn A contains 3 blue balls and 7 red balls. Urn B contains 7 blue balls and 3 red balls. Balls are now randomly drawn from one of these urns where the drawn ball is always placed back into the same urn. Twelve such random draws yielded 8 red balls and 4 blue balls. What do you estimate the probability that the balls were drawn from urn A?
2026-04-02 02:27:41.1775096861
Advanced urn problem
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Hint: Can you calculate the probability that twelve draws from $A$ gave that result? Similarly for draws from $B$? Then the probability you want is the first divided by the sum.