| Aspect | Classical | Conditional | Bayes' |
|---|---|---|---|
| When to use | Equally likely outcomes | Given event occurred | Reverse conditional |
| Formula | n(S) | P(B) | P(A|)P(A) |
| Requires | Counting techniques | Intersection and P(B) | Partition and likelihoods |
| Direction | Forward | Forward (restricted) | Backward (cause from effect) |
| JEE example | Ball drawing | Given red, P(from bag 1) | Defective item, which machine? |
| Key tool | Combinations, permutations | Multiplication rule | Total probability theorem |
| Difficulty | Easy-Medium | Medium | Medium-Hard |
When classical becomes conditional: "Two balls drawn. Given first is red, find P(second is red)" — the "given" restricts the sample space.
When conditional becomes Bayes': "A red ball is drawn. Find P(it came from Bag I)" — reversing the direction from effect to cause.
Decision rule: If the problem says "given that..." use conditional. If it asks "which source/cause" use Bayes'. If neither, use classical counting.