medium Probability
A release-checked medium problem for training Combinations and Permutations.
Three distinct integers from $[n] = \{1,2,\dots, n\}$ are selected uniformly at random, where $n$ is an odd positive integer. Find the probability that the three numbers form a arithmetic progression when $n = 15$. For example, if the three selected numbers are $26, 38,$ and $14$, this would be an arithmetic progression $14 \rightarrow 26 \rightarrow 38$ with common difference $12$.
This Probability problem is tagged Combinations and Permutations. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.
Probability · Akuna
Probability
Probability
Probability · SIG, DE Shaw
Probability · SIG, Jane Street
Probability · Jane Street