Compound events – Grade 11 math lesson

Lesson 18 of 23 in the Grade 11 math course

US version. US grades, US spelling and dollars ($). · UK Maths Department

A complete 45-minute lesson for grade 11 (ages 16–17) that runs on this page – at school or at home. Every answer is graded right away, with a worked explanation.

Time: 45 minutes + 20 min homework
Grade: Grade 11 (ages 16–17)
You need: Paper, a pencil and this page
Graded: 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 graded straight away with a worked explanation, so you never have to grade 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

Learning goal: 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	Graded by Classfern
Teaching input	10 min	Not assessed, self-checked
Worked examples and guided practice	9 min	Not assessed, graded by Classfern
Independent practice	15 min	Graded by Classfern
Closure and exit ticket	6 min	Graded by Classfern, self-checked

Starter, "your turn", practice and exit ticket are graded 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 graded instantly.

More practice

All Grade 11 math lessons and tests · Math Department

Curriculum

Common Core State Standards HSS.CP.A.2: “Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.”

Common Core State Standards HSS.CP.B.8: “(+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.”

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