Geometric Distribution Interview Questions
Geometric distribution interview prep for first-success waiting times, expected trials, biased probabilities, and memorylessness intuition.
Candidates practicing repeated-trial waiting-time questions in quant interviews.
First success model
The geometric distribution models independent repeated trials until the first success. If success probability is p each trial, the expected number of trials until success is 1/p.
Probability of first success on n
The first success on trial n means n - 1 failures followed by one success. The probability is (1 - p)^(n - 1)p.
Concrete example
For a fair coin, the probability first heads appears on flip 4 is (1/2)^3(1/2) = 1/16. The expected flips until heads is 2.
Memorylessness intuition
After failures, the process restarts if trials are independent with the same success probability. That is why the recurrence for expected waiting time is so short.
When it is not geometric
Pattern waiting times like HH or HTH are not simple first-success trials because partial progress can matter. Use states for those prompts.
Common mistakes
Candidates use geometric formulas when success probability changes or when patterns overlap. Confirm independent identical trials before applying the shortcut.
Practice the pattern
Use the LeetQuidity curriculum and calibration to turn this topic into a focused practice plan.