Probability
Term 2 starting in week 11 :: Estimated time: 2 weeks
- Know how to add, subtract and multiply fractions (review)
- Find probabilities using equally likely outcomes (review)
- Use the property that probabilities sum to 1 (review)
- Using experimental data to estimate probabilities
- Find probabilities from tables, Venn diagrams and frequency trees
- Construct and interpret sample spaces for more than one event (review)
- Calculate probability with independent events
- Use tree diagrams for independent events
- Use tree diagrams for dependent events
For higher-attaining pupils:
- Construct and interpret conditional probabilities (Tree diagrams)
- Construct and interpret conditional probabilities (Venn diagrams and two-way tables)
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Activities for pupils
Here are some related resources in alphabetical order. Some may only be appropriate for high-attaining learners while others will be useful for those in need of support. Click anywhere in the grey area to access the resource.
Venn Worksheet A collection of worksheets all related to the regions in Venn diagrams and the set notation describing them (answers included)
Pin Drop Estimate the probability of a drawing pin landing point up from experimental data.
Probability Video A reminder of how to work out basic probability leading to simple combined events and expected values.
Probability Basic probability questions in an online exercise.
Hi-Low Predictions A version of the Play Your Cards Right TV show. Calculate the probabilities of cards being higher or lower.
Predictive Survey An eight question survey collecting data for an amazing probability experiment.
Dice Investigation Throw two dice and multiply the scores. Investigate the different products you can obtain. What about adding? What about using three dice?
Venn Totals Practise reading and creating Venn diagrams containing two and three sets and the number of elements in those sets.
Dice Bingo Choose your own numbers for your bingo card. The caller uses two dice and adds the numbers together.
Venn Paint Video Here is a demonstration of how to illustrate union, intersection and complement of sets as they appear in Venn diagrams.
Tree Diagrams Video Tree diagrams can be really helpful showing combinations of two or more events in order to calculate probabilities.
Venn Paint Flood fill the regions of the Venn diagrams according to the given statements.
Tree Diagrams Calculate the probability of independent and dependent combined events using tree diagrams.
The Maths of Gambling Gambling is never a good idea and this activity might help you understand the mathematics involved.
Conditional Probability Find the probability of one event happening given that another event has already happened.
Plinko Probability A simulation of a Quincunx (Galton Board) which can be used to create the bell shaped curve of the normal distribution.
Here are some exam-style questions on this topic:
- "There are only crayons in a pencil case and the crayons are either orange, purple or brown." ... more
- "The following table shows the probabilities of winning certain prizes at a stall in Faulton Towers theme park. A prize is always given for every turn." ... more
- "The midnight train to Georgia is not the most reliable. The probability that the train will be late on any day is 0.35" ... more
- "At the Trantown annual Fayre there are a number of different sideshows designed to raise money for cancer research. Roger is looking after two of these, the lucky dip and the raffle." ... more
- "The table shows the shoe sizes of 35 male teachers." ... more
- "Carol has two fair 5-sided spinners. One spinner is pink and the other is green." ... more
- "(a) There are 24 people at a Football Club supporters' meeting in Dudley. Thirteen of them are female." ... more
- "Mrs Gill wants to give her nephew two sweets from a jar she keeps on her kitchen table. There are 11 sweets in this jar." ... more
- "Aran, Betsy and Connor collect data about which way up a drawing pin will land if dropped from a fixed height. Here are their results." ... more
- "During a demonstration for Year 10 pupils a biased coin in a computer simulation landed on heads 600 times." ... more
- "A driving test has two sections, practical(p) and theory(t). One day everyone who took the test passed at least one section. 77% passed the practical section and 81% passed the theory section." ... more
- "There are 1200 pupils at Thailand's largest British International school. 690 of these pupils are girls." ... more
- "For this question, give all your answers as fractions." ... more
- "There are some discarded marker pens in a bin." ... more
- "The Venn diagram represents a collection of 40 books on sale in an online store." ... more
- "A box contains only green and yellow crayons." ... more
- "At an international conference there were 300 delegates from both the northern and southern hemispheres. Each delegate wore a t-shirt in one of three different colours:" ... more
- "Lisa's nephew Sean has two boxes containing plastic building bricks." ... more
- "A monkey comes across a box of red and green apples in the jungle. All of the apples are the same size." ... more
- "Percy throws a fair dice until he gets a five." ... more
- "On the day after one GCSE paper Twitter and the media were buzzing with comments about a particular question about Hannah's sweets. Here is the Transum version of this now famous Maths exam question:" ... more
- "When the arrow is spun once on this spinner, a 1 or a 2 or a 3 can be scored depending on the colour the arrow lands on." ... more
- "A bag contains balls that are red, blue, green or yellow." ... more
- "There are \(x\) left shoes and 7 right shoes in a dark cupboard." ... more
- "There are only \(b\) blue counters and \(y\) yellow counters in a bag." ... more
- "On a Tuesday at a theme park, a sample of 50 visitors was randomly selected as they were leaving the park. They were asked how many times that day they had been on a ride called The Serpent. This information is summarised in the following frequency table." ... more
- "Sumville has three newspapers: The Chronicle, The Express and Moon, and The Scribe." ... more
- "900 professional footballers were surveyed with the following results" ... more
- "A game at a fayre consists of a players throwing one dart at the board pictured below.
The probability of hitting each region and the points scored for hitting that region is given in this table.
" ... more - "Julie chooses a cake from a yellow box on a shelf. The box contains two chocolate cakes and three plain cakes. She eats the cake and chooses another one from the box. The tree diagram below represents the situation with the four possible outcomes where C stands for chocolate cake and P for plain cake." ... more
- "Mathsland's national currency comes in denominations of 1 unit, 5 units, 10 units and 50 units. Sofya places this collection of these coins in her purse then, without looking, takes out two coins at random, one after the other." ... more
Here are some Advanced Starters on this statement:
- Bertrand's Box Paradox
Bertrand's box paradox is a paradox of elementary probability theory, first posed by Joseph Bertrand in 1889 more - Best Dice
Which of the unusual dice would you choose to give you the best chance of winning the prize? more - Biased Coin
Use a biased coin to obtain a fair result more - How Many Left Handers?
Work out the number of members if the probability of left-handed members being randomly selected is given. more - Other Child's Gender
What is the probability that the other child is also a boy? more - Singers and Dancers
What fraction of the singers and dancers are both singers and dancers? more - Sorcerer's Apprentices
The difference between random selection and an 'at least' scenario involving sorcerer's apprentices. more - Tri-Junction
A real life situation that can be analysed with the use of a tree diagram. more - Two Pots
Use tree diagrams to find the surprising result that probabilities of different situations are the same. more - What Question?
Write down all the possible questions that could have been asked if this was the Venn diagram provided in a mathematics exam. more
Click on a topic below for suggested lesson Starters, resources and activities from Transum.
Lesson Starters
Here are some suggestions for whole-class, projectable resources which can be used at the beginnings of each lesson in this block.
1st Lesson
Bus Stop
How many different ways can four people stand in line?
2nd Lesson
Coloured Sheep
What is the probability of picking a red sheep from the sheep in the field?
3rd Lesson
Pick From The Pot
The pot contains 10 counters which are being randomly removed and replaced. How many of each colour do you think are in the pot?
4th Lesson
Ice Cream
How many different ice cream cones can be made by choosing two scoops from six flavours?
5th Lesson
Tran's Hats
In how many different ways might Tran decide to wear his hats in one week?
6th Lesson
Refreshing Revision
It is called Refreshing Revision because every time you refresh the page you get different revision questions.
Some of the Starters above are to reinforce concepts learnt, others are to introduce new ideas while others are on unrelated topics designed for retrieval practice or and opportunity to develop problem-solving skills.
