Qm
Probability

Steps for a bug on a triangle to fall in the hole

first-passagemarkov-chain

A bug sits at corner XX of a triangle with corners XX, YY, ZZ. Each step it hops to one of the other two corners, each with probability 1/21/2. Corner ZZ has a hole: once the bug reaches ZZ it falls in and stops.

Starting at XX, on average how many hops until the bug falls in the hole?

Your answer

Solving needs a free account

Answers, streaks and solutions unlock when you are signed in. Reading the question and the hint stays free.

Create a free accountSign in

Discussion

Sign in to join the discussion · reading is open to everyone

💡 Discussion rules

  1. No full solutions here. Hints and approaches only.
  2. Complexity, edge cases and intuition are the point.
  3. Interview experiences are welcome. Respect your NDAs.

Loading discussion…

Learn the concepts

The theory behind this question.

The ABRACADABRA ProblemAcceptance-Rejection SamplingAction Spaces for Order PlacementActivist Campaigns and 13D FilingsActor-Critic Methods

Related questions

Days until a market regime crashesMoves for a robot to dock at the chargerDays until a storm arrives in a weather chainSteps for a token on a square to hit the trapdoorTaking turns to roll the first six
All questions →