MathematicsChapter 12: Basic Statistics
Probability Link (chapter List)
Chapter 12 also names probability with statistics: a probability is a number from 0 to 1.
Learning objectives
- Explain probability link (chapter list) using the correct definitions, conditions, and notation.
- Apply 0 <= P <= 1, P = favourable/total correctly in routine and exam-style questions.
- Show each important step, simplify the result, and check that it satisfies the original conditions.
Definition
Chapter 12 also names probability with statistics: a probability is a number from 0 to 1. Compound events use 'and' / 'or' with diagrams (tree, Venn) as listed in the book. Equally likely outcomes: P = favourabletotal. These notes stay at Grade 10 counting, not a university probability course.
Mathematical form
total = 6
P = favourabletotal. These notes stay
total = 6 P(even)
Where / symbols
- PROBABILITY LINK (CHAPTER LIST)
- Chapter 12 also names probability with statistics: a probability is a number from 0 to 1. Compound events use 'and' / 'or' with diagrams (tree, Venn) as listed in the book. Equally likely outcomes: P = (favourable) / (total). These notes stay at Grade 10 counting, not a university probability course.
- SINGLE EVENT
- Fair die: P(six)=1/6. Impossible 0, certain 1. Complement: P(not A)=1-P(A). Do not write 6/1.
- COMPOUND (NAMED)
- Independent 'and' multiplies in the usual school model. 'Or' for mutually exclusive adds. Trees list the sequence. Follow the chapter diagram you were taught.
Relationship
- 0 <= P <= 1
- P = favourable/total
Overview
Count, then divide:
Single Event
Fair die: P(six)=16. Impossible 0, certain 1. Complement: P(not A)=1-P(A). Do not write 61.
Examples P(six)=1/6 · P(not six)=5/6 · Not 6/1
Compound (named)
Independent 'and' multiplies in the usual school model. 'Or' for mutually exclusive adds. Trees list the sequence. Follow the chapter diagram you were taught.
Examples And vs or · Exclusive: add · Independent: multiply (school model)
WHAT — PROBABILITY LINK (CHAPTER LIST)
Chapter 12 also names probability with statistics: a probability is a number from 0 to 1. Compound events use 'and' / 'or' with diagrams (tree, Venn) as listed in the book. Equally likely outcomes: P = favourabletotal. These notes stay at Grade 10 counting, not a university probability course. The symbols and conditions are part of the mathematics, so include them when stating the rule.
WHY — Why this topic matters
Probability Link (Chapter List) matters because statistics turns raw data into useful information about position, spread, and relationship. Probability describes chance, while graphs and summary measures support fair comparisons.
HOW — How to solve and explain it
Start by identifying what is given and what must be found. Work through SINGLE EVENT, then COMPOUND (NAMED). Worked: fair six-sided die. P(even) and P(not even). even faces: 2,4,6 -> 3 outcomes total = 6 P(even) = 36 = 12 P(not even) = 1 - 12 = 12 Finish by checking signs, restrictions, units, and whether the answer matches the question.
Worked example
- fair six-sided die. P(even) and P(not even).
- even faces: 2,4,6 -> 3 outcomes
- total = 6
- P(even) = 36 = 12
- P(not even) = 1 - 12 = 12
In simple words
Probability is not the same as relative frequency in a small sample, though a long run of data should sit close. Statistics collected the data; probability models the chance.
Key points
- 0 <= P <= 1
- P = favourable/total
- favourable over total
- tree / Venn named
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Probability Link (chapter List)
Sticky Notes · Quick Revision
Core Idea
- Chapter 12 also names probability with statistics: a probability is a number from 0 to 1. Compound events use 'and' / 'or' with diagrams (tree, Venn) as listed in the book. Equally likely outcomes: P = favourabletotal. These notes stay at Grade 10 counting, not a university probability course.
SINGLE EVENT
- Fair die: P(six)=16. Impossible 0, certain 1. Complement: P(not A)=1-P(A). Do not write 61.
COMPOUND (NAMED)
- Independent 'and' multiplies in the usual school model. 'Or' for mutually exclusive adds. Trees list the sequence. Follow the chapter diagram you were taught.
Worked Method
- Worked: fair six-sided die. P(even) and P(not even).
- even faces: 2,4,6 -> 3 outcomes
- total = 6
- P(even) = 36 = 12
- P(not even) = 1 - 12 = 12
Common Misconception
- Probability is not the same as relative frequency in a small sample, though a long run of data should sit close. Statistics collected the data; probability models the chance.
FBISE Exam Check
- Probability is not the same as relative frequency in a small sample, though a long run of data should sit close. Statistics collected the data; probability models the chance.
60-second revision
- Chapter 12 also names probability with statistics: a probability is a number from 0 to 1.
- SINGLE EVENT: Fair die: P(six)=16.
- COMPOUND (NAMED): Independent 'and' multiplies in the usual school model.
- Worked-method reminder: P(not even) = 1 - 12 = 12
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