Basic Probability, Events and Counting notes for GATE DA: 31 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questions.
The Foundation. Learn to count favorable vs total outcomes using permutations and combinations.
Defining the Space. Sample spaces, unions, intersections, and complements.
Updating Beliefs. How new information changes probability. Bayes' Theorem.
Quantifying Outcomes. Discrete/continuous variables, expectation, variance.
Why start here? In competitive exams, many problems look like probability questions but are actually counting puzzles in disguise. If you cannot count the sample space correctly, the probability formula yields incorrect results.
Calculating is rarely about plugging numbers. It is almost always a Counting Problem. We use Permutations and Combinations to find and .
| Feature | Permutation | Combination |
|---|---|---|
| Question | Arrangement / Ordering | Selection / Grouping |
| Order Matters? | Yes | No |
| Formula |
Directly counting events with phrases like "at least one" often requires summing many separate cases. Instead, use the complement.
Basic Probability, Events and Counting notes for GATE DA: 31 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questions
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