The Mathematics of Maybe: Introduction to Probability: chapter on a page

A cut of Shishya's notes for this chapter: the first paragraph of the introduction and the key ideas, formulas and facts, common mistakes and quick revision lists, word for word. Nothing is added or reworded; the worked examples are left out (they are on the chapter page).

About the notes: Written by Shishya's AI on 26 Sept 2026 from the chapter's title and class level, in Shishya's own words — not a copy or summary of the textbook. Read the official chapter for the book's own text, activities and exercises.

This note's current text has no applied fact-check on record.

Mind map

Drawn from the same notes by a fixed rule (no AI): each label is the item's own words — its bold term, its label before a colon, a short formula as written, or its first words.

The mind map as a list

Key ideas
- random experiment
- outcome
- event
- Experimental probability
- Probability always lies between 0…
- As the number of trials increases…
- Probability can be expressed as a…
Formulas and facts
- Experimental probability of an event E
- P(E) = (Number of trials in which E…
- This tells you the fraction of times…
- Range of probability
- 0 ≤ P(E) ≤ 1
- A probability of 0 means the event…
- Sum rule (for complementary events)
Worked examples
- Tossing a coin
- Drawing coloured marbles
- Quality check in a factory
Watch out for
- Counting only favourable trials and…
- Writing probability greater than 1…
- Confusing outcomes with events
- Assuming experimental probability is…
- Mixing up "not E" calculations

What this chapter is about

Probability is the branch of mathematics that measures how likely an event is to happen. When you toss a coin, you cannot be certain whether it will land heads or tails, but you can say something sensible about the chances. This chapter introduces you to the language and basic calculations of probability using experiments you can actually perform.

Key ideas

A random experiment is an action whose outcome cannot be predicted with certainty, such as tossing a coin or rolling a die.
An outcome is a single possible result of an experiment; the set of all outcomes is called the sample space.
An event is any collection of one or more outcomes that we are interested in.
Experimental probability of an event equals the number of trials in which the event occurred divided by the total number of trials.
Probability always lies between 0 and 1 (inclusive). An impossible event has probability 0; a certain event has probability 1.
As the number of trials increases, the experimental probability usually becomes more stable and approaches a fixed value.
Probability can be expressed as a fraction, a decimal or a percentage.

Formulas and facts to remember

Experimental probability of an event E:
P(E) = (Number of trials in which E happened) / (Total number of trials)
This tells you the fraction of times the event occurred out of all the trials you performed.
Range of probability:
0 ≤ P(E) ≤ 1
A probability of 0 means the event never happened in any trial; a probability of 1 means it happened in every trial.
Sum rule (for complementary events):
P(E) + P(not E) = 1
If you know how often something happened, subtract from 1 to find how often it did not happen.
Converting forms:
To convert a fraction to a percentage, multiply by 100. For example, 3/10 = 0.3 = 30 %.

Common mistakes

Counting only favourable trials and forgetting to divide by total trials → Always use the formula: favourable trials divided by total trials.
Writing probability greater than 1, such as 120/100 → Check that your numerator never exceeds your denominator; probability cannot exceed 1.
Confusing outcomes with events → An outcome is a single result; an event may include several outcomes (e.g., getting an even number on a die is the event containing 2, 4, 6).
Assuming experimental probability is exact → Remember it is an estimate based on trials; more trials generally give a better estimate.
Mixing up "not E" calculations → Subtract the probability of E from 1; do not subtract the frequency from 1.

Quick revision

Experimental probability = (favourable trials) / (total trials).
Probability always lies between 0 and 1.
P(E) + P(not E) = 1.
More trials usually lead to a more stable probability estimate.
Express probability as a fraction, decimal or percentage — all are correct.
A random experiment is one whose result cannot be known in advance.