Independence vs Mutually Exclusive in Interviews
A practical guide to distinguishing independent and mutually exclusive events in probability interviews, with examples and checks.
Candidates who make event-relationship mistakes under interview pressure.
Two different relationships
Independent events do not change each other probabilities. Mutually exclusive events cannot happen together. These are different statements about the same sample space.
The quick test
For independence, check whether P(A and B) equals P(A)P(B). For mutually exclusive events, check whether P(A and B) equals 0.
Concrete example
On one fair die roll, rolling a 1 and rolling a 2 are mutually exclusive. They are not independent because knowing a 1 occurred makes the probability of a 2 equal to 0.
Nontrivial overlap matters
If two events with positive probability are mutually exclusive, they cannot be independent. The product P(A)P(B) is positive, while P(A and B) is zero.
Interview wording
Say the events in plain English before using formulas. Many mistakes come from treating no overlap, no influence, and negative correlation as interchangeable.
Common mistakes
Candidates often assume disjoint events are independent because they look clean on a diagram. In fact, disjoint positive-probability events strongly inform each other.
Practice the pattern
Use the LeetQuidity curriculum and calibration to turn this topic into a focused practice plan.