← Maths
Probability
Probability · 7 Sections

Probability

Master coins, dice, cards and the addition & multiplication rules — every concept, formula and shortcut tested in SSC CGL, CHSL, CAT and UPSC.

1
Section 1 of 7

What is Probability? — Sample Space, Events & P = F/T

Probability measures how likely an event is to occur. It is always a number between 0 (impossible) and 1 (certain). The core formula is:

P(E) = Number of Favourable Outcomes / Total Number of Outcomes
Sample Space (S)Set of all possible outcomesCoin: S = {H, T}. Die: S = {1,2,3,4,5,6}. Two coins: S = {HH,HT,TH,TT}.
EventA subset of the sample spaceSimple event = 1 outcome. Compound event = more than 1 outcome. Impossible event: P = 0. Sure event: P = 1.
Equally Likely OutcomesEach outcome has the same probabilityA fair coin — P(H) = P(T) = 1/2. A fair die — P(1) = P(2) = ... = P(6) = 1/6.
Range of Probability0 ≤ P(E) ≤ 1Sum of probabilities of all elementary events = 1. Negative probability is impossible.
Probability SimulatorInteractive experiments
H
Heads
0
Heads
—%
0
Tails
—%
Theoretical: P(H) = P(T) = 1/2 = 50%
Total flips: 0
Key terms: Elementary event — only one outcome. Exhaustive events — their union equals the full sample space. Favourable outcomes — outcomes that satisfy the condition of the event.

A bag has 4 red and 6 blue balls. Total outcomes = . (4 red + 6 blue = 10 total)

Probability of getting a head on a fair coin flip is: (1 favourable outcome ÷ 2 total outcomes = 1/2)

A die is thrown. P(getting a 3) = . (1 favourable ÷ 6 total = 1/6)

📝Practice Questions

Q1A bag has 5 red and 3 blue balls. What is P(red)?

Q2A die is thrown once. What is P(getting a number greater than 4)?

Q3Which of the following can be the probability of an event?

🔒
Section 2 of 7

Complementary Events — P(not A) = 1 − P(A)

Complete section 1 above to unlock this section.

🔒
Section 3 of 7

Mutually Exclusive Events & Addition Rule P(A∪B)

Complete section 2 above to unlock this section.

🔒
Section 4 of 7

Independent Events & Multiplication Rule P(A∩B)

Complete section 3 above to unlock this section.

🔒
Section 5 of 7

Coins & Dice Problems — Sample Spaces & Results

Complete section 4 above to unlock this section.

🔒
Section 6 of 7

Card Problems — 52-Card Deck Structure & Probabilities

Complete section 5 above to unlock this section.

🔒
Section 7 of 7

Exam Shortcuts, Complement Method & SSC Patterns

Complete section 6 above to unlock this section.

📚

Every Question Type — Solved

10 question types · 20 solved examples from real SSC papers

SSC probability splits into ten distinct question shapes. Below is one clean, verified example for each shape — tap to reveal the worked solution and see exactly how the examiner thinks.

How to solve this type
P(event) = favourable outcomes / total outcomes. First count every object in the bag to get the total; then count only the objects that satisfy the condition. For "not X" questions use the complement: P(not X) = 1 − P(X). The #1 trap is forgetting one category when summing the total — list every colour/type and add them all before dividing.

A bag contains 6 white, 8 black, 4 red and 3 blue marbles. One marble is drawn at random. The probability that it is black or blue is:

A9/21B11/21C1/3D7/21

A bag contains 5 red, 3 white and 2 green balls. One ball is drawn at random. The probability that it is NOT red is:

A1/2B3/5C2/5D1/5