medium Probability
A release-checked medium problem for training Conditional Expectation, Expected Value.
You have been arrested and need to post bail. You have a bag of $\$100$ bills of which one half are real and the other half are fake. You need to pay $\$500$ for bail. Every time you give the jail a fake bill, the funds you have given are given back to you and you need to start again. How many bills will you have to pull out of the bag on average? Assume the probability of drawing each type of bill is constant per trial.
This Probability problem is tagged Conditional Expectation, Expected Value. 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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