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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?

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Christmas activities make those December Maths lessons interesting, exciting and relevant. If students have access to computers there are some online activities to keep them engaged such as Christmas Ornaments and Christmas Light Up.


"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."

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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.


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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.

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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