JEEClass 11-12
Probability Formulas for JEE
All Probability formulas for JEE Maths — from basic counting to Bayes' theorem and binomial distribution.
Basic Probability
ClassicalP(E) = n(E)/n(S)
ComplementP(E') = 1 − P(E)
Addition ruleP(A∪B) = P(A) + P(B) − P(A∩B)
For 3 eventsP(A∪B∪C) = ΣP(A) − ΣP(A∩B) + P(A∩B∩C)
Mutually exclusiveP(A∩B) = 0 ⇒ P(A∪B) = P(A) + P(B)
Conditional Probability
DefinitionP(A|B) = P(A∩B) / P(B)
Multiplication ruleP(A∩B) = P(B) · P(A|B)
Independent eventsP(A∩B) = P(A) · P(B)
Total probabilityP(B) = Σ P(B|Aᵢ) · P(Aᵢ)
Bayes' theoremP(Aᵢ|B) = P(B|Aᵢ)·P(Aᵢ) / ΣP(B|Aⱼ)·P(Aⱼ)
Binomial Distribution
P(X = k)P(X=k) = nCk · pᵏ · qⁿ⁻ᵏ, q = 1−p
MeanE(X) = np
VarianceVar(X) = npq
Std deviationσ = √(npq)
Mode(n+1)p − 1 ≤ mode ≤ (n+1)p
P(at least 1)P(X ≥ 1) = 1 − P(X=0) = 1 − qⁿ
JEE Tips
- Tip 1:For 'at least one' problems, always use complementary counting: 1 − P(none)
- Tip 2:Bayes' theorem: identify the partition (causes) and the event (effect), then apply formula
- Tip 3:In binomial distribution, the mode is the most probable number of successes