Probability — Part 1: Sample space, events and the classical definition: visual lesson, ICSE Class 10 Mathematics

Lesson

Probability, Part 1

Measuring how likely an event is, with a number from $0$ to $1$ .

In this lesson you will

List the sample space of a random experiment
Distinguish elementary, sure and impossible events
Calculate a probability as favourable over total outcomes
Use P(not E) = 1 − P(E)

From experiment to probability in four steps.

Concept

What you will be able to do

List the sample space of a random experiment
Name elementary, sure and impossible events
Find $P(E)$ as favourable over total outcomes
Use the complement: $P(\text{not } E) = 1 - P(E)$

The five words of probability.
Term	Meaning
Random experiment	an experiment whose result cannot be predicted in advance
Outcome	one possible result
Sample space	the set of all possible outcomes
Event	a set of outcomes that we are interested in
Equally likely	no outcome is favoured over another

Concept

Random experiments and the sample space

A random experiment has results that cannot be predicted in advance. Each result is an outcome; the set of all outcomes is the sample space $S$ .

The sample space lists every possible outcome once.
Experiment	Sample space	Outcomes
Toss one coin	$\{H, T\}$	$2$
Toss a coin twice, noting the order	$\{HH, HT, TH, TT\}$	$4$
Throw one die	$\{1, 2, 3, 4, 5, 6\}$	$6$
Draw one card from a pack	$13$ ranks in each of $4$ suits	$52$
Draw one ball from $3$ red and $2$ blue	the five balls	$5$

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