Venn diagrams and conditional probability – Year 9 maths lesson
Lesson 24 of 38 in the Year 9 maths course
UK version. UK school years, UK spelling and pounds (£). · US Math Department
A complete 45-minute lesson for Year 9 (ages 13–14) that runs on this page – at school or at home. Every answer is marked straight away, with a worked explanation.
- Time
- 45 minutes + 20 min homework
- Year
- Year 9 (ages 13–14)
- You need
- Paper, a pencil and this page
- Marked
- Instantly, with explanations
For parents: how to use this lesson
You don't need to know this topic yourself. The lesson explains each step on screen, one tidy step at a time. Every answer is marked straight away with a worked explanation, so you never have to mark anything.
- Read what your child will learn and the big ideas together.
- Press Start the lesson below and sit with your child for the teaching and the worked examples (about 19 minutes).
- Let them do the practice on their own. They choose Getting started, On track or Challenge – start on On track and move up after a few right in a row.
- Finish with the exit ticket and the talk question: “What is the difference between P(A and B) and P(A given B)?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Counting the overlap twice. Fill in the overlap first, then subtract it from each set.
- Using the whole total for a conditional probability. Given B: divide by the number in B only.
Tip for home: Sort a pile of objects into a Venn diagram using two rules.
What your child will learn
We are learning to use Venn diagrams, set notation and two-way tables to find probabilities.
Success looks like
- I can complete a Venn diagram.
- I can use set notation.
- I can find a conditional probability.
Key words
- set
- a collection of items
- intersection
- in both sets (∩)
- union
- in either set or both (∪)
- conditional probability
- probability given that something else has happened
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Survey the family: who likes tea, who likes coffee, both or neither. Draw a Venn diagram.
The big ideas (for the adult)
A Venn diagram sorts items into sets. The overlap is in both sets: A ∩ B. Everything in A or B is A ∪ B.
Fill a Venn diagram from the middle outwards, so the overlap is not counted twice.
Conditional probability is the probability of A given B has happened: only look at the items in B.
The lesson, step by step
| Part | Time | How it is checked |
|---|---|---|
| Starter: quick recall | 5 min | Marked by Classfern |
| Teaching input | 10 min | Not assessed, self-checked |
| Worked examples and guided practice | 9 min | Not assessed, marked by Classfern |
| Independent practice | 15 min | Marked by Classfern |
| Plenary and exit ticket | 6 min | Marked by Classfern, self-checked |
Starter, "your turn", practice and exit ticket are marked by Classfern. Worked examples and teaching are not assessed. The hands-on task and the reflection are self-assessed. Explanations in talk are judged by the parent and not recorded.
The lesson
It runs here on the page. No sign-up and no names – progress is kept only in this browser.
Homework and practice at home
20 minutes: 10 practice questions, 3 multiple-choice questions and 2 to remember from earlier work, then a short reflection. New questions every time, all marked instantly.
More practice
More Year 9 maths lessons
- Prime factors, HCF and LCM
- Rounding and estimation
- Bounds and error intervals
- Standard form
- Laws of indices
- Powers and roots
- Units and measures
- Area of triangles, parallelograms and trapeziums
- Circles: circumference, area, arcs and sectors
- Volume and surface area
- Angle facts and parallel lines
- Angles in polygons
- Pythagoras' theorem
- Trigonometry: SOH CAH TOA
- Transformations
- Similarity and congruence
- Quadrilaterals and symmetry
- Coordinate geometry
- 3-D shapes, plans and elevations
- Quartiles, box plots and spread
- Pie charts and time series graphs
- Sampling
- Relative frequency and expected outcomes
- Algebraic notation
- Substitution
- Simplifying expressions
- Expanding brackets
- Solving linear equations
- Inequalities
- Rearranging formulae
- Sequences and the nth term
- Straight-line graphs
- Graphs of functions
- Ratio
- Percentages
- Speed, density and pressure
- Scale drawings and maps
Curriculum
National Curriculum for England, Year 9: “enumerate sets and unions/intersections of sets systematically, using tables, grids and Venn diagrams”
GCSE subject content P6: “enumerate sets and combinations of sets systematically, using tables, grids, Venn diagrams and tree diagrams”
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Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.