easy Probability
A release-checked easy problem for training Conditional Expectation, Dice.
Alice repeatedly rolls a standard fair 6-sided die. If she obtains $1,2,$ or $3$, she receives $\$1$ and rolls again. If she obtains $4$ or $5$, she receives $\$1$ and ends the game. If she obtains a $6$, the game ends and Alice loses all of her money. Find Alice's expected payout from this game.
This Probability problem is tagged Conditional Expectation, Dice. 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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