Probability - How It Appears in JEE

6 recurring patterns. Learn the pattern, recognize it in 5 seconds, apply the right approach.

Pattern

Find probability given a condition or constraint

How to recognize

Phrases like 'given that', 'if it is known that', 'among those who', or conditional setup

→ Identify the condition (B) and the event (A). Use P(A|B) = P(A∩B)/P(B). Reduce sample space to B first.

Pattern

Find the probability of a cause given the effect

How to recognize

Multiple sources/causes, an outcome is observed, find which source produced it

→ Identify partitions E₁...Eₙ. Compute P(Eᵢ)·P(A|Eᵢ) for each. Apply Bayes formula.

Pattern

n independent trials with fixed success probability

How to recognize

Coin toss, die throw, repeated experiments with same probability, mean/variance of distribution

→ Identify n, p, q. Use P(X=r) = nCr·p^r·q^(n-r). Mean = np, Var = npq.

Pattern

Find expected value, variance, or probability distribution of a random variable

How to recognize

Asks for E(X), Var(X), probability distribution table, or expected winnings/losses

→ List all values of X with their probabilities. E(X) = Σxᵢ·P(xᵢ). Var = E(X²) - [E(X)]².

Pattern

Problems involving independence, union, intersection of events

How to recognize

Multiple events, asks for P(at least one), P(exactly k), or uses independence condition

→ P(at least one) = 1 - P(none). For independent events, P(A∩B) = P(A)·P(B). Use inclusion-exclusion for unions.

Pattern

Probability using permutations/combinations for sample space and favorable outcomes

How to recognize

Drawing balls, selecting items, arranging objects, dice sums

→ Count favorable outcomes and total outcomes using PnC. P = favorable/total. Ensure equally likely outcomes.