Probability Inequalities for Interviews
Probability inequalities interview prep for Markov, Chebyshev, simple tail bounds, loose-versus-exact reasoning, and misuse cases.
Advanced candidates who need bounds when exact probabilities are hard.
Why bounds matter
Probability inequalities give guaranteed bounds when an exact probability is hard or when only limited information is available.
Markov intuition
Markov inequality bounds the chance that a nonnegative random variable is large using only its expectation. It is broad but often loose.
Chebyshev intuition
Chebyshev inequality bounds the chance of being far from the mean using variance. It works widely, but it can be much weaker than a distribution-specific tail estimate.
Concrete example
If a nonnegative variable has expected value 10, Markov says the probability it is at least 50 is at most 10/50. The true probability could be much smaller.
Compare with exact tails
If you know the full distribution, exact or approximated tail probabilities may be sharper. Bounds are most useful when distribution detail is limited.
Common mistakes
Candidates often treat a bound as an estimate. A bound says no more than this much, not approximately this much.
Practice the pattern
Use the LeetQuidity curriculum and calibration to turn this topic into a focused practice plan.