easy Probability
A release-checked easy problem for training Conditional Probability.
Suppose that $X_1,X_2,\dots, X_n$ are IID continuous random variables and $1 \leq k \leq n$. Define $M_r = \max\{X_1,\dots, X_r\}$. Find $\prob{X_k = M_n \mid X_k = M_k}$ when $k = 10$ and $n = 25$. In other words, given that $X_k$ is the largest random variable among the first $k$, find the probability it is the largest among all of the random variables.
This Probability problem is tagged Conditional Probability. 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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