Math · Statistics and Probability

Probability formulas for JEE

Every Probability formula you need for JEE, grouped by concept.

15 formulas4 concepts

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QuestionState the formula — Addition Theorem (2 Sets)

Reveal answer

Addition Theorem (2 Sets)

P(A \cup B) = P(A) + P(B) - P(A \cap B)

Probability of occurrence of at least one of two events.addition-theoremunion

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All 15 Probability formulas

Conditional & Independent Events

9 formulas

Addition Theorem (2 Sets)

P(A \cup B) = P(A) + P(B) - P(A \cap B)

Probability of occurrence of at least one of two events.

addition-theoremunion

Addition Theorem (3 Sets)

P(A \cup B \cup C) = P(A) + P(B) + P(C) - P(A \cap B) - P(B \cap C) - P(A \cap C) + P(A \cap B \cap C)

Probability of occurrence of at least one of three events.

additionunion-three

Classical Definition of Probability

P(E) = \frac{n(E)}{n(S)}

Probability of an event E evaluated using the count of favorable outcomes.

applies whenAll elementary outcomes in the sample space S must be equally likely.

classicalbasic

Complementary Event

P(A') = 1 - P(A)

Probability of the non-occurrence of event A.

complementbasic

Conditional Probability

P(A|B) = \frac{P(A \cap B)}{P(B)}

Probability of event A occurring given that event B has already occurred.

applies when

P(B) > 0

conditionaljee-advanced

De Morgan's Law in Probability

P(A' \cap B') = 1 - P(A \cup B)

Probability of neither event A nor event B occurring.

demorgancomplement

Probability of Exactly One Event

P(A \cap B') + P(A' \cap B) = P(A) + P(B) - 2P(A \cap B)

Probability that exactly one of the two events A or B occurs.

symmetric-differenceexact

Independent Events Condition

P(A \cap B) = P(A) P(B)

The defining condition for two events to be statistically independent.

applies whenEvents A and B are strictly independent.

independencejee-advanced

Multiplication Theorem

P(A \cap B) = P(A) P(B|A)

Probability of the simultaneous occurrence of two dependent events.

applies when

P(A) > 0

multiplicationjee-advanced

Total Probability and Bayes' Theorem

2 formulas

Bayes' Theorem

P(E_i|A) = \frac{P(E_i) P(A|E_i)}{\sum_{j=1}^{n} P(E_j) P(A|E_j)}

Calculates the reverse conditional probability of partition E_i given outcome A.

applies whenPartitions

E_i

must be mutually exclusive and exhaustive,

P(A) > 0

bayesjee-advanced

Law of Total Probability

P(A) = \sum_{i=1}^{n} P(E_i) P(A|E_i)

The total probability of an event A across all exhaustive partitions of the sample space.

applies whenPartitions

E_i

must be mutually exclusive and exhaustive.

total-probabilityjee-advanced

Random Variables & Variance

3 formulas

Axiomatic Probability Sum

\sum_{i=1}^{n} P(\omega_i) = 1

The sum of probabilities of all elementary events in a sample space equals 1.

applies whenAll

\omega_i

form a mutually exclusive and exhaustive sample space.

axiomaticpmf

Expected Value (Mean)

\mu = E(X) = \sum_{i} x_i p_i

The expected value or mean of a discrete random variable.

applies when

\sum p_i = 1

meanexpected-valuejee-advanced

Variance of a Random Variable

\sigma^2 = Var(X) = \sum_{i} x_i^2 p_i - \mu^2

The variance of a discrete probability distribution.

variancedispersionjee-advanced

Bernoulli Trials and Binomial Distribution

1 formula

Binomial Probability Distribution

P(X=r) = \binom{n}{r} p^r q^{n-r}

Probability of exactly r successes in n independent Bernoulli trials.

applies whenIndependent trials, two possible outcomes per trial, constant success probability p, and

p+q=1

binomialbernoullijee-advanced

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