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Class 12 Statistics Notes · GSEB

Types of Events

Probability — learn certain, impossible, complementary, elementary, and compound events with Venn diagrams and examples. GSEB Class 12 Statistics notes.

Last updated: 25 Aug 2026

Notes

Types of Events

In probability, an event is a subset of the sample space. Events come in different types depending on their likelihood and composition.

Certain, Impossible, and Complementary Events

Certain Event
An event that will definitely happen. It equals the entire sample space S. P(S) = 1. Rolling a die → getting a number ≤ 6 is certain.
Impossible Event
An event that can never happen. It is the empty set ∅. P(∅) = 0. Rolling a die → getting 7 is impossible.
Complementary Event
All outcomes in S that are NOT in event A. Written as A'. P(A') = 1 − P(A). If A = even, then A' = odd on a die.

Think about it

When you appear for your GSEB exam, "scoring above 100%" is impossible, "scoring between 0 and 100" is certain, and "scoring below 40" is complementary to "scoring 40 or above."

Elementary and Compound Events

TypeDefinitionExample (Die Roll)Number of outcomes
ElementaryA single outcome{3} — getting exactly 3Exactly 1
CompoundTwo or more outcomes{2, 4, 6} — even numbers2 or more
Every elementary event has probability P = 1/n(S) when outcomes are equally likely. For a fair die, each face has P = 1/6.

Explore: Event Types with Venn Diagram

Select an event definition below, then toggle the visibility buttons to see how A, A', and S relate in the Venn diagram.

Event Types — Venn Diagram
SA

A = {2, 4, 6}

A' = {1, 3, 5}

n(A) + n(A') = 3 + 3 = 6 = n(S)

3/6
P(A)
3/6
P(A')
1
P(S)

Sure, Possible, and Impossible — The Probability Scale

Impossible → 0
1 → Certain
P = 0 (Impossible)P = 0.5P = 1 (Certain)
Impossible
P = 0
Rolling a 7 on a die
Possible
0 < P < 1
Getting heads on a coin
Certain
P = 1
Getting ≤ 6 on a die

Key Takeaways

Key Takeaways

  • An event is any subset of the sample space — it can be a single outcome or a collection.
  • Certain events (P = 1) always happen; impossible events (P = 0) never happen.
  • The complement A' contains everything in S that is NOT in A, and P(A') = 1 − P(A).
  • Elementary events have exactly one outcome; compound events have two or more.
  • Every probability lies between 0 and 1: 0 ≤ P(A) ≤ 1.

Practice

  1. A die is rolled. Let A = {1, 3, 5}. Write A' and find P(A').
  2. Is the event "getting a number greater than 10" on a die certain, impossible, or possible?
  3. If P(A) = 0.35, what is P(A')? What does A' represent in words?

Explore Further