| Property | Independent | Mutually Exclusive |
|---|---|---|
| Definition | P(AB) = P(A)*P(B) | P(AB) = 0 |
| Intuition | A doesn't affect B | A and B can't co-occur |
| P(A|B) | = P(A) | = 0 |
| P(A union B) | P(A)+P(B)-P(A)P(B) | P(A)+P(B) |
| Complement | A',B' also independent | A',B' NOT mutually exclusive |
| Relationship | Can co-occur | Cannot co-occur |
| Venn diagram | Overlapping circles | Non-overlapping circles |
Critical fact: If P(A) > 0 and P(B) > 0, then:
- Mutually exclusive implies DEPENDENT (not independent)
- Independent implies NOT mutually exclusive (they can co-occur)
Why this matters in JEE: Questions frequently test whether students confuse these concepts. Common trap: "A and B are mutually exclusive, find P(A intersect B)" — students who think "exclusive = independent" will compute P(A)*P(B) instead of 0.
Three events: Pairwise independence does NOT imply mutual independence. All four conditions (three pairwise + triple) must hold.