easy Probability
A release-checked easy problem for training Conditional Probability, Discrete Random Variables.
Three riflemen $X ,Y$ and $Z$ take turns shooting at a target. $X$ shoots first, $Y$ second, and $Z$ third, after which the cycle repeats with $X$ again and again, until one of the riflemen hits the target. Each shot hits the target with probability $50\%$, independent of other shots. Find the probability $X$ wins.
This Probability problem is tagged Conditional Probability, Discrete Random Variables. 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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