Negative Binomial Interview Questions
Negative binomial interview prep for waiting until the r-th success, geometric and binomial connections, expectations, and parameterization traps.
Candidates extending geometric-distribution reasoning to repeated successes.
The waiting-time question
Negative binomial reasoning appears when a prompt asks how long it takes to get the r-th success in repeated independent trials.
Connection to geometric
The geometric distribution is the special case where r equals 1. Negative binomial extends that idea from first success to r-th success.
Concrete example
For fair coin flips, the number of flips needed to get the third head follows a negative-binomial waiting-time pattern. The final flip must be a head, and the earlier flips contain exactly two heads.
Expectation intuition
If each success has probability p, the expected number of trials to get r successes is r divided by p. This follows from adding r geometric waiting stages.
Parameterization matters
Some sources count total trials until r successes, while others count failures before r successes. In interviews, state which version you are using.
Common mistakes
Candidates often use the binomial distribution for a fixed number of trials when the prompt actually asks for a random waiting time.
Practice the pattern
Use the LeetQuidity curriculum and calibration to turn this topic into a focused practice plan.