Transum Software

Probability Formulae

Show that you know which formula to use for each probability question. A drag and drop challenge.

You did it!

\(P(A) = \frac{n(A)}{n(U)}\)


\(P(A \cup B)=P(A) + P(B) - P(A \cap B)\)

\(P(A \cup B)=P(A) + P(B)\)

\(P(A|B) = \frac{P(A\cap B}{P(B)}\)

\(P(A \cap B) = P(A)P(B)\)

Drag each formula above onto the problem they can help solve.

There are 25 students in the class.
Five of these students are in a band.
If a student is picked at random from the class, what is the probability that they are in the band?

The probability that the train will be on time is 0.7
What is the probability the train will not be on time?

What is the probability of getting a head or a six when rolling a fair dice and tossing a normal, unbiased coin.

The probability that a student at a school is under 13 is 0.3
The probability that a student at the same school is over 16 is 0.2
If a student is picked at random from the school, what is the probability that they are either under 13 or over 16?

There are 10 red and 5 blue watches in a bag.
5 of the red watches are faulty.
3 of the blue watches are faulty.
A watch is picked out of the bag and is seen to be faulty. What is the probability that it is red given that it is faulty?

The probability that it will rain tomorrow is 0.7
The probability that a student in this class will have their birthday tomorrow is 0.45
What is the probability that both of these events will happen?

This web site contains over a thousand free mathematical activities for teachers and pupils. Click here to go to the main page which links to all of the resources available.

Please contact me if you have any suggestions or questions.

Email address

Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

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 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"

Each month a newsletter is published containing details of the new additions to the Transum website and a new puzzle of the month.

The newsletter is then duplicated as a podcast which is available on the major delivery networks. You can listen to the podcast while you are commuting, exercising or relaxing.

Transum breaking news is available on Twitter @Transum and if that's not enough there is also a Transum Facebook page.

Featured Activity

Online Logo

Online Logo

An opportunity for students to write a computer program. There is nothing to download, all of the interaction takes place in the browser. Great for understanding angles and the properties of shapes.


"Numeracy is a proficiency which is developed mainly in Mathematics but also in other subjects. It is more than an ability to do basic arithmetic. It involves developing confidence and competence with numbers and measures. It requires understanding of the number system, a repertoire of mathematical techniques, and an inclination and ability to solve quantitative or spatial problems in a range of contexts. Numeracy also demands understanding of the ways in which data are gathered by counting and measuring, and presented in graphs, diagrams, charts and tables."

Secondary National Strategy, Mathematics at key stage 3

Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths main page links to more activities designed for students in upper Secondary/High school.


If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:

Alternatively, if you use Google Classroom, all you have to do is click on the green icon below in order to add this activity to one of your classes.

It may be worth remembering that if should go offline for whatever reason, there are mirror sites at and that contain most of the resources that are available here on

When planning to use technology in your lesson always have a plan B!

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.


©1997-2021 WWW.TRANSUM.ORG

© Transum Mathematics 1997-2021
Scan the QR code below to visit the online version of this activity.

This is a QR Code

Description of Levels



Level 1 - Drag the questions to match the formulae

Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

More on this topic including lesson Starters, visual aids, investigations and self-marking exercises.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

Log in Sign up


You may also want to use a calculator to check your working. See Calculator Workout skill ##.

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

Log in Sign up