Combined events and tree diagrams – Year 10 maths lesson

Lesson 21 of 37 in the Year 10 maths course

UK version. UK school years, UK spelling and pounds (£). · US Math Department

A complete 45-minute lesson for Year 10 (ages 14–15) 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 10 (ages 14–15)
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: “Why do the probabilities on each set of branches add up to 1?”
Later that day or the next day: the homework (20 minutes), then a practice test.

Watch out for

Adding along branches instead of multiplying. Along: multiply. Between routes: add.
Keeping the same probabilities when items are not replaced. Reduce the total by one on the second set of branches.

Tip for home: Work out the chances in a simple game with two dice.

What your child will learn

We are learning to find probabilities of combined events with sample spaces and tree diagrams.

Success looks like

I can list a sample space.
I can use a tree diagram.
I can deal with events without replacement.

Key words

sample space: a list of all possible outcomes
tree diagram: branches showing each stage of events
independent: one event does not affect the other
without replacement: not put back, so the next probability changes

What to have ready

Paper and a pencil
This page on a computer, tablet or phone
For the hands-on part: Draw a tree diagram for picking two socks from a drawer, with and without putting the first back.

The big ideas (for the adult)

A sample space lists every possible combined outcome, for example a grid for two dice.

On a tree diagram, multiply along the branches to find the probability of one route; add the routes you need.

Without replacement, the second set of branches changes because there is one fewer item.

The lesson, step by step

45 minutes in 5 parts
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

All Year 10 maths lessons and tests · Maths Department

Curriculum

National Curriculum for England, Year 10: “calculate the probability of independent and dependent combined events, including using tree diagrams and other representations, and know the underlying assumptions”

GCSE subject content P8: “calculate the probability of independent and dependent combined events, including using tree diagrams and other representations, and know the underlying assumptions”

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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.