 # Probability Formulae

## You did it!

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

$$P(A)+P(A')=1$$

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

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

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

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

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?

## Transum.org

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. ## More Activities:

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 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 14 October 'Starter of the Day' page by Inger Kisby, Herts and Essex High School:

"Just a quick note to say that we use a lot of your starters. It is lovely to have so many different ideas to start a lesson with. Thank you very much and keep up the good work."

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#### Nine Digits Arrange the given digits one to nine to make three numbers such that two of them add up to the third. This is a great puzzle for practicing standard pen and paper methods of three digit number addition and subtraction.

## Numeracy

"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.

## Teachers

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:

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

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

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Scan the QR code below to visit the online version of this activity. https://Transum.org/go/?Num=859

## Description of Levels

Close 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.

## Example

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.

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