Probability formulas

Every formula JEE Advanced expects you to know for Probability, with the variables spelled out. Free, no sign-up. Read it before a mock, not during one.

Practise these formulas 313 practice questions

Formulas: 34
Subject: Mathematics
Exam: JEE Advanced
No sign-in needed: ₹0

Probability, every formula

34 formulas, typeset and free. Print it, or keep it open beside your practice.

Classical definition
$P (A) = \frac{n ( A )}{n ( S )} = \frac{m}{n}$
favourable / total
Range of probability
$0 \leq P (A) \leq 1$
Complement
$P (\overset{ˉ}{A}) = 1 - P (A)$
Impossible & certain events
$P (\emptyset) = 0, P (S) = 1$
Odds in favour of A
$P (A) : P (\overset{ˉ}{A})$
Probability from odds x:y
$P (A) = \frac{x}{x + y}, P (\overset{ˉ}{A}) = \frac{y}{x + y}$
Addition theorem
$P (A \cup B) = P (A) + P (B) - P (A \cap B)$
Mutually exclusive addition
$P (A \cup B) = P (A) + P (B)$
A∩B=∅
Addition for three events
$P (A \cup B \cup C) = \sum P (A) - \sum P (A \cap B) + P (A \cap B \cap C)$
Exactly one of A, B
$P (A) + P (B) - 2 P (A \cap B)$
De Morgan (neither)
$P (\overset{ˉ}{A} \cap \overset{ˉ}{B}) = 1 - P (A \cup B)$
De Morgan (not both)
$P (\overset{ˉ}{A} \cup \overset{ˉ}{B}) = 1 - P (A \cap B)$
Conditional probability
$P (B ∣ A) = \frac{P ( A \cap B )}{P ( A )}, P (A) \neq = 0$
Multiplication theorem
$P (A \cap B) = P (A) P (B ∣ A) = P (B) P (A ∣ B)$
Independent events
$P (A \cap B) = P (A) P (B)$
Independent — union
$P (A \cup B) = 1 - P (\overset{ˉ}{A}) P (\overset{ˉ}{B})$
Independence of complements
$A, B independent \Rightarrow \overset{ˉ}{A}, \overset{ˉ}{B} independent$
Law of total probability
$P (A) = i \sum P (E_{i}) P (A ∣ E_{i})$
E_i partition of S
Bayes' theorem
$P (E_{i} ∣ A) = \frac{P ( E _{i} ) P ( A ∣ E _{i} )}{\sum _{j} P ( E _{j} ) P ( A ∣ E _{j} )}$
Geometric probability
$P = \frac{measure of favourable region}{measure of whole region}$
n coins: exactly r heads
$P = \frac{^{n} C _{r}}{2 ^{n}}$
n coins: at least one head
$P = 1 - \frac{1}{2 ^{n}}$
Two dice: sum k (favourable)
$k - 1 (2 \leq k \leq 7), 13 - k (8 \leq k \leq 12)$
out of 36
Derangement probability (n envelopes)
$P = \frac{1}{n !} (all correct), 1 - \frac{1}{n !} (at least one wrong)$
Binomial probability
$P (X = r) =^{n} C_{r} p^{r} q^{n - r}, q = 1 - p$
Binomial mean
$μ = n p$
Binomial variance
$σ^{2} = n pq$
Binomial S.D.
$σ = n pq$
Binomial: mean > variance
$mean > variance (∵ q < 1)$
Most probable number of successes
$r = ⌊(n + 1) p ⌋ (mode)$
Mean of a random variable
$μ = E (X) = \sum x_{i} P (x_{i})$
Variance of a random variable
$σ^{2} = \sum x_{i}^{2} P (x_{i}) - μ^{2}$
Sum of probabilities
$i \sum P (x_{i}) = 1$
P(A∩B) when A⊆B
$A \subseteq B \Rightarrow P (A) \leq P (B)$

Know the Probability formulas. Now use them.

Formulas only stick when you apply them under time. Adaptive practice picks the concept you keep dropping marks on.

Create a free account All formula sheets

Join QuestPix, Today!

Get notified first, with exam & curriculum updates, course & test series launch offers, motivation & success stories and free learning resources recommended by toppers.

Probability formulas

Probability, every formula

Classical definition

Range of probability

Complement

Impossible & certain events

Odds in favour of A

Probability from odds x:y

Addition theorem

Mutually exclusive addition

Addition for three events

Exactly one of A, B

De Morgan (neither)

De Morgan (not both)

Conditional probability

Multiplication theorem

Independent events

Independent — union

Independence of complements

Law of total probability

Bayes' theorem

Geometric probability

n coins: exactly r heads

n coins: at least one head

Two dice: sum k (favourable)

Derangement probability (n envelopes)

Binomial probability

Binomial mean

Binomial variance

Binomial S.D.

Binomial: mean > variance

Most probable number of successes

Mean of a random variable

Variance of a random variable

Sum of probabilities

P(A∩B) when A⊆B

More JEE Advanced Mathematics formula sheets

Know the Probability formulas. Now use them.

Join QuestPix, Today!