Transum Maths Software


There are 366 different Starters of The Day, many to choose from. You will find in the left column below some starters on the topic of Probability. In the right column below are links to related online activities, videos and teacher resources.

A lesson starter does not have to be on the same topic as the main part of the lesson or the topic of the previous lesson. It is often very useful to revise or explore other concepts by using a starter based on a totally different area of Mathematics.

Main Page

Probability Starters:

Bus Stop: How many different ways can four people stand in line?

Coloured Sheep: What is the probability of picking a red sheep from the sheep in the field?

Ice Cream: How many different ice cream cones can be made by choosing two scoops from six flavours?

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?

Tran's Hats: In how many different ways might Tran decide to wear his hats in one week?


Small images of these Starters ::  Index of Starters

Probability Advanced Starters:

Airport Security: The old lady has a misconception about conditional probability

Bertrand's Box Paradox: Bertrand's box paradox is a paradox of elementary probability theory, first posed by Joseph Bertrand in 1889

Best Dice: Which of the unusual dice would you choose to give you the best chance of winning the prize?

Biased Coin: Use a biased coin to obtain a fair result

Ghosts or Papua New Guinea: A probability prediction based on a biased sample

How Many Left Handers?: Work out the number of members if the probability of left-handed members being randomly selected is given.

Other Child's Gender: What is the probability that the other child is also a boy?

Perennial Rivals: Which football team will be first to win four games?

Sorcerer's Apprentices: The difference between random selection and an 'at least' scenario involving sorcerer's apprentices.

Tri-Junction: A real life situation that can be analysed with the use of a tree diagram.

Two Pots: Use tree diagrams to find the surprising result that probabilities of different situations are the same.

Unfinished Game: Share the prize in a fair ratio according to the probability of each player winning.

What Question?: Write down all the possible questions that could have been asked if this was the Venn diagram provided in a mathematics exam.

Index of Advanced Starters


Probability Washing Line

Probability Washing Line

Hang out the washing on the line so that the probability words on the t-shirts are in order.

The short web address is:


Curriculum for Probability:

Years 7 to 9

Pupils should be taught to record, describe and analyse the frequency of outcomes of simple probability experiments involving randomness, fairness, equally and unequally likely outcomes, using appropriate language and the 0-1 probability scale more...

Pupils should be taught to understand that the probabilities of all possible outcomes sum to 1 more...

Pupils should be taught to generate theoretical sample spaces for single and combined events with equally likely, mutually exclusive outcomes and use these to calculate theoretical probabilities more...

Years 10 and 11

Pupils should be taught to apply the property that the probabilities of an exhaustive set of mutually exclusive events sum to 1 more...

Pupils should be taught to use a probability model to predict the outcomes of future experiments; understand that empirical unbiased samples tend towards theoretical probability distributions, with increasing sample size more...

Pupils should be taught to calculate the probability of independent and dependent combined events, including using tree diagrams and other representations, and know the underlying assumptions more...

Pupils should be taught to {calculate and interpret conditional probabilities through representation using expected frequencies with two-way tables, tree diagrams and Venn diagrams} more...

Years 12 and 13

Pupils should be taught to understand and use mutually exclusive and independent events when calculating probabilities. Link to discrete and continuous distributions more...

Pupils should be taught to understand and use simple, discrete probability distributions (calculation of mean and variance of discrete random variables is excluded), including the binomial distribution, as a model; calculate probabilities using the binomial distribution more...

Pupils should be taught to understand and use conditional probability, including the use of tree diagrams, Venn diagrams, two-way tables. Understand and use the conditional probability formula P(A|B)=P(A∩B)/P(B) more...

Pupils should be taught to understand and use the Normal distribution as a model; find probabilities using the Normal distribution. Link to histograms, mean, standard deviation, points of inflection and the binomial distribution more...

Pupils should be taught to conduct a statistical hypothesis test for the proportion in the binomial distribution and interpret the results in context. Understand that a sample is being used to make an inference about the population and appreciate that the significance level is the probability of incorrectly rejecting the null hypothesis more...

Pupils should be taught to modelling with probability, including critiquing assumptions made and the likely effect of more realistic assumptions more...

Pupils should be taught to select an appropriate probability distribution for a context, with appropriate reasoning, including recognising when the binomial or Normal model may not be appropriate more...

Pupils should be taught to conduct a statistical hypothesis test for the mean of a Normal distribution with known, given or assumed variance and interpret the results in context more...

International Baccalaureate

See the Statistics and Probability sub-topics, syllabus statements, exam-style questions and learning resources for the IB AA course here.

Exam-Style Questions:

There are almost a thousand exam-style questions unique to the Transum website.


Comment recorded on the s /Coordinate 'Starter of the Day' page by Greg, Wales:

"Excellent resource, I use it all of the time! The only problem is that there is too much good stuff here!!"

Comment recorded on the 26 March 'Starter of the Day' page by Julie Reakes, The English College, Dubai:

"It's great to have a starter that's timed and focuses the attention of everyone fully. I told them in advance I would do 10 then record their percentages."

Comment recorded on the 19 November 'Starter of the Day' page by Lesley Sewell, Ysgol Aberconwy, Wales:

"A Maths colleague introduced me to your web site and I love to use it. The questions are so varied I can use them with all of my classes, I even let year 13 have a go at some of them. I like being able to access Starters for the whole month so I can use favourites with classes I see at different times of the week. Thanks."

Comment recorded on the 1 May 'Starter of the Day' page by Phil Anthony, Head of Maths, Stourport High School:

"What a brilliant website. We have just started to use the 'starter-of-the-day' in our yr9 lessons to try them out before we change from a high school to a secondary school in September. This is one of the best resources on-line we have found. The kids and staff love it. Well done an thank you very much for making my maths lessons more interesting and fun."

Comment recorded on the 19 June 'Starter of the Day' page by Nikki Jordan, Braunton School, Devon:

"Excellent. Thank you very much for a fabulous set of starters. I use the 'weekenders' if the daily ones are not quite what I want. Brilliant and much appreciated."

Comment recorded on the 10 April 'Starter of the Day' page by Mike Sendrove, Salt Grammar School, UK.:

"A really useful set of resources - thanks. Is the collection available on CD? Are solutions available?"

Comment recorded on the 14 September 'Starter of the Day' page by Trish Bailey, Kingstone School:

"This is a great memory aid which could be used for formulae or key facts etc - in any subject area. The PICTURE is such an aid to remembering where each number or group of numbers is - my pupils love it!

Comment recorded on the 7 December 'Starter of the Day' page by Cathryn Aldridge, Pells Primary:

"I use Starter of the Day as a registration and warm-up activity for my Year 6 class. The range of questioning provided is excellent as are some of the images.
I rate this site as a 5!"

Comment recorded on the 18 September 'Starter of the Day' page by Mrs. Peacock, Downe House School and Kennet School:

"My year 8's absolutely loved the "Separated Twins" starter. I set it as an optional piece of work for my year 11's over a weekend and one girl came up with 3 independant solutions."

Comment recorded on the 28 May 'Starter of the Day' page by L Smith, Colwyn Bay:

"An absolutely brilliant resource. Only recently been discovered but is used daily with all my classes. It is particularly useful when things can be saved for further use. Thank you!"

Comment recorded on the 17 November 'Starter of the Day' page by Amy Thay, Coventry:

"Thank you so much for your wonderful site. I have so much material to use in class and inspire me to try something a little different more often. I am going to show my maths department your website and encourage them to use it too. How lovely that you have compiled such a great resource to help teachers and pupils.
Thanks again"

Comment recorded on the 1 August 'Starter of the Day' page by Peter Wright, St Joseph's College:

"Love using the Starter of the Day activities to get the students into Maths mode at the beginning of a lesson. Lots of interesting discussions and questions have arisen out of the activities.
Thanks for such a great resource!"

Comment recorded on the 23 September 'Starter of the Day' page by Judy, Chatsmore CHS:

"This triangle starter is excellent. I have used it with all of my ks3 and ks4 classes and they are all totally focused when counting the triangles."

Comment recorded on the 2 April 'Starter of the Day' page by Mrs Wilshaw, Dunsten Collage,Essex:

"This website was brilliant. My class and I really enjoy doing the activites."

Comment recorded on the 9 October 'Starter of the Day' page by Mr Jones, Wales:

"I think that having a starter of the day helps improve maths in general. My pupils say they love them!!!"

Comment recorded on the 19 October 'Starter of the Day' page by E Pollard, Huddersfield:

"I used this with my bottom set in year 9. To engage them I used their name and favorite football team (or pop group) instead of the school name. For homework, I asked each student to find a definition for the key words they had been given (once they had fun trying to guess the answer) and they presented their findings to the rest of the class the following day. They felt really special because the key words came from their own personal information."

Comment recorded on the 3 October 'Starter of the Day' page by S Mirza, Park High School, Colne:

"Very good starters, help pupils settle very well in maths classroom."

Comment recorded on the 9 April 'Starter of the Day' page by Jan, South Canterbury:

"Thank you for sharing such a great resource. I was about to try and get together a bank of starters but time is always required elsewhere, so thank you."

Comment recorded on the 21 October 'Starter of the Day' page by Mr Trainor And His P7 Class(All Girls), Mercy Primary School, Belfast:

"My Primary 7 class in Mercy Primary school, Belfast, look forward to your mental maths starters every morning. The variety of material is interesting and exciting and always engages the teacher and pupils. Keep them coming please."

Comment recorded on the 11 January 'Starter of the Day' page by S Johnson, The King John School:

"We recently had an afternoon on accelerated learning.This linked really well and prompted a discussion about learning styles and short term memory."

Comment recorded on the 17 June 'Starter of the Day' page by Mr Hall, Light Hall School, Solihull:

"Dear Transum,

I love you website I use it every maths lesson I have with every year group! I don't know were I would turn to with out you!"

Comment recorded on the 5 April 'Starter of the Day' page by Mr Stoner, St George's College of Technology:

"This resource has made a great deal of difference to the standard of starters for all of our lessons. Thank you for being so creative and imaginative."

Comment recorded on the 16 March 'Starter of the Day' page by Mrs A Milton, Ysgol Ardudwy:

"I have used your starters for 3 years now and would not have a lesson without one! Fantastic way to engage the pupils at the start of a lesson."

Comment recorded on the 28 September 'Starter of the Day' page by Malcolm P, Dorset:

"A set of real life savers!!
Keep it up and thank you!"

Comment recorded on the s /Indice 'Starter of the Day' page by Busolla, Australia:

"Thank you very much for providing these resources for free for teachers and students. It has been engaging for the students - all trying to reach their highest level and competing with their peers while also learning. Thank you very much!"

Comment recorded on the 25 June 'Starter of the Day' page by Inger.kisby@herts and, :

"We all love your starters. It is so good to have such a collection. We use them for all age groups and abilities. Have particularly enjoyed KIM's game, as we have not used that for Mathematics before. Keep up the good work and thank you very much
Best wishes from Inger Kisby"

Comment recorded on the 6 May 'Starter of the Day' page by Natalie, London:

"I am thankful for providing such wonderful starters. They are of immence help and the students enjoy them very much. These starters have saved my time and have made my lessons enjoyable."

Comment recorded on the 12 July 'Starter of the Day' page by Miss J Key, Farlingaye High School, Suffolk:

"Thanks very much for this one. We developed it into a whole lesson and I borrowed some hats from the drama department to add to the fun!"

Comment recorded on the 10 September 'Starter of the Day' page by Carol, Sheffield PArk Academy:

"3 NQTs in the department, I'm new subject leader in this new academy - Starters R Great!! Lovely resource for stimulating learning and getting eveyone off to a good start. Thank you!!"

Comment recorded on the 3 October 'Starter of the Day' page by Fiona Bray, Cams Hill School:

"This is an excellent website. We all often use the starters as the pupils come in the door and get settled as we take the register."


Probability is a measure of the weight of evidence, and is arrived at through reasoning and inference. In simple terms it is a measure or estimation of likelihood of the occurrence of an event. The word probability comes from the Latin word probabilitas which is a measure of the authority of a witness in a legal case. Some of the earlier mathematical studies of probability were motivated by the desire to be more profitable when gambling. Today however the practical uses of probability theory go far beyond gambling and are used in many aspects of modern life.

We believe that even adults can, in many cases, have a poor intuition regarding the effects of probability. These activities are designed to help pupils calculate but also get a 'feel' for the principles of probability.

Probability Teacher Resources:

Dice and Spinners: Computer generated random numbers for games and probability experiments

Probability Words: A visual aid to highlight the vocabulary of probability and to debate the relationship between the given words.

Likelihood: Arrange some statements in order according to the probability of them happening. Compare your opinion with thousands of others.

Skunk: A game for the whole Maths class to play involving chance and choice.

Greater Than: The teacher is in charge of the order in which the numbered cards are revealed. Pupils have to decide where to put them!

Snail Race Projectable: Twelve snails have a race based on the sum of two dice. This is the teachers' version of the race simulation.

Two Dice Possibility Space: An interactive visual aid showing the possibility space obtained when throwing two dice

Dice Bingo: Choose your own numbers for your bingo card. The caller uses two dice and adds the numbers together.

Normal Distribution Calculator: A customised online calculator for quickly finding areas under the normal distribution curve.

Significance: A slide presentation showing how to use the chi-squared test to measure significance.

Plinko Probability: A simulation of a Quincunx (Galton Board) which can be used to create the bell shaped curve of the normal distribution.

t-Test Revision: A slide presentation designed to revise the key aspects of Student's t-Test.

Probability Activities:

Probability Washing Line: Hang out the washing on the line so that the probability words on the t-shirts are in order.

Pin Drop: Estimate the probability of a drawing pin landing point up from experimental data.

Likelihood: Arrange some statements in order according to the probability of them happening. Compare your opinion with thousands of others.

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.

Remainder Race: A game involving chance and choice requiring an ability to calculate the remainder when a two digit number is divided by a single digit number.

Superior: A game for two players who compete to make the largest possible number from randomly selected cards.

Snail Race: A race between 12 snails. Which snail is most likely to win? This is the students' version of the race simulation.

Great Expectation: An interactive online activity requiring logical thinking and a certain amount of luck to place the digits on the correct side of the inequality sign.

Frequency Trees: Use a frequency tree to show two or more events and the number of times they occurred.

Pascal's Triangle: Get to know this famous number pattern with some revealing learning activities

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.

Probability Formulae: Show that you know which formula (as given in the IB Formula Booklet) to use for each probability question. A drag and drop challenge.

Finally there is Topic Test, a set of 10 randomly chosen, multiple choice questions suggested by people from around the world.

Alternatively, for the more advanced student, there is an ever-growing collection of Exam-Style Questions with worked solutions on the topic of Probability.

Probability Investigations:

Egg Box Investigation: In how many different ways can two eggs be arranged in an egg box?

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?

Traffic Jams: How many ways can three cars be lined up in a traffic jam?

House Painting: The houses in Mathsland are all three storeys tall. Each storey is painted using one colour. How many ways can the houses be painted?

Beginning with One: Is it true that most numbers begin with the digit one? Think of numbers you see everyday and it is a surprising fact that so many of them begin with a one. Can you think why this is true?

Probability Videos:

Probability video
Transum's Probability Video

Probability Video: A reminder of how to work out basic probability leading to simple combined events and expected values.

Calculator Dice Video: If you have no dice don't despair because most scientific calculators have a random number generating facility as can be seen in this short video.

Tree Diagrams Video: Tree diagrams can be really helpful showing combinations of two or more events in order to calculate probabilities.

GCSE Probability Part 1: Screencast of probability lesson for Intermediate GCSE Maths.

Statistical Significance: This video explains numeric and categorical data and helps you gain an understanding of when to apply a t-test or a chi-square test.

Probability Worksheets/Printables:

Snail Race Board: If pupils are unable to play the Snail Race online this printable board can be used with counters and dice.

Pascal's Triangle Worksheet: Various forms of Pascal's Triangle ready for printing.

Probability External Links:

Links to other websites containing resources for Probability are provided for those logged into 'Transum Mathematics'. Subscribing also opens up the opportunity for you to add your own links to this panel. You can sign up using one of the buttons below:


The activity you are looking for may have been classified in a different way from the way you were expecting. You can search the whole of Transum Maths by using the box below.






Is there anything you would have a regular use for that we don't feature here? Please let us know.


Probability Formulae

Probability Formulae

Show that you know which formula (as given in the IB Formula Booklet) to use for each probability question. A drag and drop challenge.

The short web address is:


Teaching Notes:

Many Transum activities have notes for teachers suggesting teaching methods and highlighting common misconceptions. There are also solutions to puzzles, exercises and activities available on the web pages when you are signed in to your Transum subscription account. If you do not yet have an account and you are a teacher, tutor or parent you can apply for one by completing the form on the Sign Up page.

A Transum subscription also gives you access to the 'Class Admin' student management system, downloadable worksheets, many more teaching resources and opens up ad-free access to the Transum website for you and your pupils.


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M. F. Kuali, Mount Fletcher

Thursday, March 29, 2012

"I like this topic because it helps one to predict the the future outcomes of most of the events happening in the world , e . g . weather focus."

Fiona McDonnell, Twitter

Sunday, January 16, 2022


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