Study SimplifyStudy Simplify

Class 12 Statistics Notes · GSEB

Random Experiment and Sample Space

Probability — learn what a random experiment is, its three characteristics, and how to write the sample space with sample points. GSEB Class 12 Statistics notes.

Last updated: 25 Aug 2026

Practice Sums →

Notes

Random Experiment and Sample Space

A random experiment is any process whose .

Words marked with a dotted underline carry the question they usually appear in — tap them to reveal it.

Deterministic vs Random Experiments

AspectDeterministicRandom
OutcomeAlways the sameCannot be predicted
ExampleSun rises in the eastTossing a coin
RepetitionSame result every timeMay give different results
Probability needed?NoYes

Real-life connection

Your daily commute is not deterministic — traffic, signals, and weather make it random. A factory machine producing identical bolts is deterministic (ideally), but checking whether a bolt is defective is random.

What Makes an Experiment 'Random'?

Random Experiment
An experiment where all possible outcomes are known, but the exact outcome cannot be predicted before performing it. Three conditions must hold: (1) The set of all possible outcomes is known. (2) More than one outcome is possible. (3) The result cannot be predicted with certainty.

Random — Rolling a die

You know the outcomes are 1, 2, 3, 4, 5, 6.

Not random — Boiling water

Water always boils at 100°C (at sea level). The outcome is certain — not a random experiment.

Sample Space and Sample Points

Sample Space (S)
. Each individual outcome is called a sample point (or elementary outcome). The sample space is the collection of all sample points.
Coin toss: S = {H, T}, n(S) = 2
Die roll: S = {1, 2, 3, 4, 5, 6}, n(S) = 6

Explore: Build Your Own Sample Space

Select an experiment from the buttons below. The sample space appears inside the box. Click individual outcomes to form an event — watch n(A) and P(A) update live.

Sample Space Builder

Two coins tossed — four equally likely outcomes.

Sample Space S — n(S) = 4
Click outcomes to form an event.

Finite vs Infinite Sample Spaces

TypeDescriptionExamplen(S)
FiniteCoin toss, die rollCountable (2, 6, 36...)
InfiniteUnlimited possible valuesHeight of a personUncountable

Exam note

GSEB questions almost always use finite sample spaces. When you see "infinite," .

Key Takeaways

Key Takeaways

  • A random experiment has known possible outcomes but an unpredictable result.
  • The sample space S is the set of ALL possible outcomes; each outcome is a sample point.
  • n(S) counts the total number of outcomes — this is the denominator in classical probability.
  • Finite sample spaces have countable outcomes (coins, dice); .
  • Writing the correct sample space is the FIRST step in solving any probability problem.

Check Your Recall

Check Your Recall

3 questions
1

Write the sample space of a random experiment of throwing one balanced die and a balanced coin simultaneously.

1 mark
2

State the number of sample points in the random experiment of tossing one balanced coin and two balanced dice simultaneously.

1 mark
3

Two cards are selected one by one with replacement from 52 cards. State the number of elements in the sample space of this random experiment.

2 marks

Practice

  1. Write the sample space for drawing one card from a standard 52-card deck. What is n(S)?
  2. A bag contains 3 red and 2 blue balls. Two balls are drawn one after another WITHOUT replacement. Write S and find n(S).
  3. Is "measuring the temperature at noon in Ahmedabad" a finite or infinite sample space? Why?

Explore Further

Related Questions

Study Simplify Special

View All