Compound Probability Mental Math
Compound probability mental math for repeated events, complements, survival probabilities, small-probability approximations, and independence checks.
Candidates practicing repeated trials, survival probabilities, and complements.
Repeated events need structure
For repeated trials, decide whether events are independent and whether the question asks for all, none, at least one, or exactly k successes.
Complements are often fastest
At least one success is usually easier as one minus no successes. This avoids listing every path with one or more successes.
Concrete example
For ten independent events with 1 percent chance each, probability of at least one is 1 - 0.99^10, which is roughly 10 percent for quick intuition.
Check independence
Multiplication shortcuts require independence or a stated conditional model. If outcomes influence each other, build the dependence into the calculation.
Common mistakes
Candidates often multiply probabilities because the prompt repeats. Repetition alone does not guarantee independence, so state the dependency assumption first.
Practice the pattern
Use the LeetQuidity curriculum and calibration to turn this topic into a focused practice plan.