medium Probability
A release-checked medium problem for training Combinations and Permutations, Dice.
Two dice with the values $1-n$ on the sides are rolled, with side $i$ having probability $p_i$ of appearing. You are to choose $p_1,\dots, p_n$ in any way you'd like, but they must be common between the two dice. What is the minimum probability that the two dice show the same value? Report the answer for $n = 10$.
This Probability problem is tagged Combinations and Permutations, Dice. 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