Experimental probability – Grade 11 math lesson

Lesson 17 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: “If you flip a coin 10 times and get 7 heads, is the coin biased?”
Later that day or the next day: the homework (20 minutes), then a practice test.

Watch out for

Thinking a few trials prove a dice is unfair. Small samples vary: do many more trials.
Expecting exactly the expected number every time. Expected is an average, not a promise.

Tip for home: Do a quick experiment with a dice and record results together.

What your child will learn

Learning goal: estimate probabilities from experiments and predict expected outcomes.

Success looks like

I can calculate relative frequency.
I can predict expected outcomes.
I can decide whether something might be biased.

Key words

experimental probability: how often something happened as a fraction of the trials
trial: one go of an experiment
expected: the number you would predict
fair: all outcomes equally likely

What to have ready

Paper and a pencil
This page on a computer, tablet or phone
For the hands-on part: Flip a coin 50 times, record the results and work out the relative frequency of heads after 10, 20 and 50 flips.

The big ideas (for the adult)

Relative frequency = number of times something happened ÷ number of trials. It estimates the probability.

The more trials, the better the estimate.

Expected number of outcomes = probability × number of trials.

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.IC.A.2: “Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model?”

Common Core State Standards HSS.MD.B.6: “(+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).”

Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.