Poisson Approximation to Binomial Interview Questions
Poisson approximation to binomial interview prep for rare successes, lambda equals np, approximation conditions, and limits.
Candidates practicing rare-event and approximation problems.
When the approximation appears
Poisson approximation is useful for binomial counts with many trials, small success probability, and a moderate expected count.
Match lambda to np
For a Binomial(n, p) count, the Poisson approximation uses lambda = np. That preserves the expected number of successes.
Concrete example
If there are 1,000 independent trials with success probability 0.002, the expected count is 2, so a Poisson model with lambda 2 may be a useful approximation.
Why it helps
The Poisson formula can be simpler than a binomial expression when n is large and p is small.
Approximation limits
The approximation can be poor when p is not small, trials are dependent, or the count is in a region where binomial shape matters.
Common mistakes
Candidates often use Poisson because the count is large. The small probability and independence assumptions matter too.
Practice the pattern
Use the LeetQuidity curriculum and calibration to turn this topic into a focused practice plan.