medium Probability
A release-checked medium problem for training Games, Bayes' Theorem, Conditional Probability, Expected Value/LOTUS.
Jesse has an urn with $2$ white and $3$ black balls. He randomly draws balls out of the urn without replacement; he has the option to stop drawing at any time. For every white ball he draws, he earns $\$1$, but for every black ball he draws, he loses $\$1$. Suppose Jesse draws balls following the optimal strategy. What is his expected loss or gain?
This Probability problem is tagged Games, Bayes' Theorem, Conditional Probability, Expected Value/LOTUS. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.
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