Quant interview prep guides

Recursive Probability Interview Questions

Recursive probability interview prep for first-step setup, state equations, boundary conditions, random walks, and dice games.

Candidates practicing dice, random walk, and state-based probability prompts.

When recursion helps

Recursive probability helps when the problem after one step looks like a smaller or shifted version of the original problem.

Define states

A good recurrence starts by defining what state you are in. The state should contain enough information to make the next-step probabilities clear.

First-step setup

Condition on the next roll, flip, move, or draw. Write the target probability from the current state as a weighted average of probabilities from next states.

Boundary conditions

Boundaries anchor the recurrence. For example, a hitting probability is 1 at the target state and 0 at a losing absorbing state.

Concrete example shape

In a random walk hitting problem, the probability of eventual success from position i can be written using the probabilities from neighboring positions after one move.

Common mistakes

Candidates often write equations before defining states. Name the state and boundary values first, then write the recurrence.

Practice the pattern

Use the LeetQuidity curriculum and calibration to turn this topic into a focused practice plan.