Conditional probability – Grade 11 math lesson
Lesson 19 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: “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
Learning goal: 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 | 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
More Grade 11 math lessons
- Complex numbers
- Radicals
- Vectors
- Laws of exponents
- Square roots and cube roots
- Systems of equations
- Rational expressions and polynomials
- Arithmetic and geometric sequences
- Iteration
- Functions
- Graphing functions
- Exponential functions
- Trigonometric functions
- Law of sines and law of cosines
- Coordinate geometry
- Counting outcomes
- Experimental probability
- Compound events
- Expected value
- Box plots and interquartile range
- Scatter plots and lines of fit
- Sampling and making inferences
Curriculum
Common Core State Standards HSS.CP.A.4: “Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results.”
Common Core State Standards HSS.CP.A.1: “Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ("or," "and," "not").”
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.