Basic Probability, Events and Counting Short Notes for GATE DA: Concepts, Formulas, Worked Examples & Practice

Basic Probability, Events and Counting short notes for GATE DA: 3 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questions.

Quick Recap: Counting for Probability

Core Takeaways

1

Classical Probability $P (E) = n (E) / n (S)$ requires equally likely outcomes.
2

Selection Use $(r n)$ when order does not matter.
3

Complement $P (At least one) = 1 - P (None)$ .
4

Integer Solutions Non-negative: $(k - 1 n + k - 1)$ | Positive: $(k - 1 n - 1)$
5

Subsets Total subsets of $n$ elements = $2^{n}$ . Use binary choice logic.

Quick Recap: Event Operations

Core Takeaways

Sample Space: Set of all outcomes.
Union / Intersect: OR / AND.
Mutually Exclusive: $P (A \cap B) = 0$ .
Independent: $P (A \cap B) = P (A) P (B)$ .
At Least One: $1 - P (None)$ .
De Morgan's: $(A \cup B)^{'} = A^{'} \cap B^{'}$ .

Last-Minute Sheet: Poisson Limits

Core formula

P (Y = k) = \frac{e ^{- λ} λ ^{k}}{k !}, E [Y] = Var (Y) = λ

Two limits

$Bin (n, p) n \to \infty, p \to 0, n p = λ Poisson (λ)$
$\frac{Y _{λ} - λ}{λ} λ \to \infty N (0, 1)$

Exam checklist

Rare events, moderate $λ$ → use Poisson directly.
Cumulative sum with growing parameter → CLT on Poisson.
At-least questions → compute via $1 - P (Y \leq k - 1)$ .
Never mix the two limits; read whether $n p$ is fixed or $λ \to \infty$ .

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Basic Probability, Events and Counting Short Notes for GATE DA: Concepts, Formulas, Worked Examples & Practice

Basic Probability, Events and Counting short notes for GATE DA: 3 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice ques

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