Venn diagrams and probability RAG. Make sure you are happy with the following topics before continuing. Complete the Venn diagram. Example: We have the numbers \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11\}. This means that \frac{7}{10} of the 70 students play football only and \frac{3}{10} of the 70 students play rugby only. • This is an OR probability problem! Once you’ve mastered these, feel free to move on to the more complicated stuff. The Venn diagram shows information about a coin collection. 3. Step 2: Numbers that are odd but aren’t prime: 1 and 9. PLEASE NOTE: This navigation system is still under development. Probability meets Problem Solving! We can write this as the following fraction: Question 2: All the students in year 10 were asked if they study geography or history. Read each question carefully before you begin answering it. This type of activity is known as Practice. These will go in the part of section A that doesn’t intersect with B. We are told that the ratio of the number of students who play football only to the number of students who play rugby only is 7 : 3. August 1, 2018 Craig Barton. Key Learning: It is important to carefully list the conditions given in the question in the form of a Venn diagram. www.justmaths.co.uk Venn Diagrams (H) - Version 2 January 2016 5. Videos, worksheets, 5-a-day and much more Tes Global Ltd is Resources made by expert teachers. 5. Previous topic Next topic. Going back to the probability question, ' Calculate P(A), P(A ∩ B) and P(B') ' you can see there are 9 elements in the universal set. The ratio of the students that only play football to the students that only play rugby is 7 : 3. a)  Fill in the Venn diagram to show the above information. 30 students are asked if they have a dog or cat. Venn Diagram Worksheets, Questions and Revision Level 6-7 . a)  Draw a Venn diagram to show the above information. (We are dealing in tenths here because the sum of the ratio is 10.). We are also told that 42 students play both sports, so we can write ‘42’ in the intersection of the two circles. Categories & Ages. b)  What is the probability that this student only likes hippos? A Venn diagram is a picture that represents the outcomes of an experiment. 8.2 Venn Diagrams & 2 way tables Easy Hard. This will be true for any mutually exclusive events since they never overlap in the Venn diagram. The Ultimate Collection of ALL questions on VENN DIAGRAMS from EdExcel 1MA1 9-1 GCSE Mathematics - FREE. Looking at the Venn diagram, we see that 4 of the 11 numbers are in both A and B, so the probability of a number being both odd and prime is, \dfrac{4}{11}. Complete differentiated lesson with the same starter and plenary to check for progress made throughout the lesson. What is the probability that this student studies both history and geography? Clearly, therefore, for two events A and B, P(A) + P(B) - P(AÇB) = P(AÈB) 14 students do not play rugby or football. The above 2, 3 and 4 circle Venn diagram examples aim to make you understand better the whole idea behind this diagrams. Read our guide, All the students that study geography only (, All the students that study history only (, All the students that study both geography and history (, All the students that study neither history nor geography (. If we know someone takes History, then they must be one of the 2+12=14 people. We are looking for all numbers that are in set A but not set B, 1 and 9, which gives a probability of, \dfrac{2}{11}. The 36 that study neither subject are the ones that do not study history, so 36 out of the 88 who do not study geography do not study history. Home Edexcel GCSE Maths Topic Questions 8. Even fluent English speakers can get confused in these problems; observing how a student new to the language misinterprets details can also help us see how anyone new to Venn problems might think. In this topic you will learn how to construct a Venn diagram and then how to use a Venn diagram to determine probabilities. www.justmaths.co.uk Venn Diagrams (F) - Version 3 January 2016 Venn Diagrams (F) A collection of 9-1 Maths GCSE Sample and Specimen questions from AQA, OCR, Pearson-Edexcel and WJEC Eduqas. While solving such questions, avoid taking many variables. In this activity students are presented with a real-world scenario. Question 1: There are 126 students in year 9.  6. A tree diagram use branches to show the different outcomes of experiments and makes complex probability questions easy to visualize. You then have to use the given information to populate the diagram and figure out the remaining information. Easy Marks: 4 . 4. Mathematics / Data and statistics / Data representation, Expanding Brackets -EdExcel 1MA1 questions. Question 3: 80 students in year 4 are asked about whether they like sharks, crocodiles or hippos. b)  What fraction of year 9 play rugby only? As you see, the Venn diagram formula can help you to find solutions for a variety of problems and questions from the real life. Video transcript. Creative Commons "Sharealike" Other resources by this author. Addition rule for probability. A Venn diagram consists of multiple overlapping closed curves, usually circles, each representing a set. All questions from past papers, specimen papers, sample papers are included. 1a; 1b; 2a; 2b; 3a; 3b; 4; Question 1a . Another type of questions asked from this topic is based on maxima and minima. Venn Diagram Word Problems - Three Sets. 1. Check your answers seem right. The Ultimate Collection of ALL questions on VENN DIAGRAMS from EdExcel 1MA1 9-1 GCSE Mathematics - FREE.All questions from past papers, specimen papers, sample papers are included. Clues and fully worked model solutions/answers available free from mathsupgrade.co.uk. Step 1: Identify numbers that are odd: \{1, \, 3, \, 5, \, 7, \, 9, \, 11 \} and numbers that are prime: \{2, \, 3, \, 5, \, 7, \, 11 \}. A Venn diagram is a simple but powerful way to represent the relationships between datasets. (A new question of the week) I mentioned that we have had a number of questions related to Venn diagrams recently. This question is simple enough to answer without a Venn diagram but it can be less confusing when visualising some of the combined events. A typical Venn diagram looks like the picture below. The probability of a certain event occurring, for example, can be represented by P(A). a)  What need to input the data. In this topic you will learn how to construct a Venn diagram and then how to use a Venn diagram to determine probabilities. The answer of 22.5\% is also acceptable.). ξ = 120 coins in the collection T = coins from the 20th century B = British coins A coin is chosen at random. Venn diagrams are helpful for thinking about probability … Email. Attempt every question. View Answer Watch Solution. Diagnostic Questions; SSDD Problems; Maths Venns; My blog; Medium blog posts; My books; Podcast; Twitter; Talks and workshops ; Probability from Venn diagrams. It is British.  2. Example-Problem Pair. Put the odd numbers in A and prime numbers in B. Draw Venn diagram using the information provided and answer the questions that follow. Some of the data we are going to input will be easy, other parts may be more confusing. The probability of a different event occurring can be written P(B). Here is a Venn diagram. Easy Questions Download PDF Quick Answers. Venn diagrams are used to determine conditional probabilities. Assess your score No idea Unsure Got it. Created: Aug 20, 2020| Updated: Aug 29, 2020. Probability 8.2 Venn Diagrams & 2 way tables. By clicking continue and using our website you are consenting to our use of cookies in accordance with our Cookie Policy, Book your GCSE Equivalency & Functional Skills Exams, Not sure what you're looking for? There’s some crossover here: \{3, \, 5, \, 7, \, 11\} are contained in both, which means they go in the intersection. • 8 have a dog, but not a cat. London WC1R 4HQ. A number is selected at random. • 21 have a dog. Step 3: All the numbers that are neither odd nor prime: 4, 6, 8, and 10, will go inside the rectangle but outside either circle. And for the sake of this video, we're going to assume that our deck has no jokers in it. Drawing Venn diagrams is relatively simple as shown below. For instance: Out of forty students, 14 are taking English Composition and … 50 students were asked in a survey whether they use texts or social media. This website and its content is subject to our Terms and A B AB Example: If A = band members and B = club members, find the probability of AUB in the school. Probability can be studied in conjunction with set theory, with Venn Diagrams being particularly useful in analysis. Then, there are 12 out of those 14 people who take Geography, or in other words. Venn Diagrams Exam Questions Grade 10 & 11 Presented by Jurgens Basson . Since there are 126 students in total, of which 14 play neither sport and of which 42 play both sports, we can work out how many students play football or rugby only: Now that we know that a total of 70 students play only football or only rugby, we are now in a better position to work out exactly how many students fall into each category. Probability with Venn diagrams. 30 students are asked if they have a dog or cat. We have a range of learning resources to compliment our website content perfectly. We can express this as the following fraction: (You could give the probability as a decimal or as a percentage (the question doesn’t state how the answer should be given), but since both the decimal (0.0985….) It generally consists of a box that represents the sample space We want to find the probability that someone takes Geography given that we already know they take History. Example: In the Venn diagram below, G represents students selecting Geography and H represents students selecting History. 40 x KS3 Maths Homework Sheets / Booklet WITH ANSWERS!!!! a)  The first thing we need to do is draw a rectangle labelled \xi to represent all the year 9 students. Venn Diagrams www.naikermaths.com Probability : Venn Diagrams - Edexcel Past Exam Questions 1. Easy Marks: 2 . 1. • 16 have a cat. 8 lessons in Sets, Venn and sample space diagrams: Venn diagrams; Set notation 1; Overlapping circles (Part 1) Overlapping circles (Part 2) Venn Diagram and probability; Drawing Venn Diagrams; Using Venn diagrams for conditional probability; Mixed questions with Venn Diagrams Complete the Venn diagram. c)  There are 44 students in total that like crocodiles. Don’t spend too long on one question. I give out the exam questions at the start of the lesson, and the first student to answer correctly during the lesson wins a prize (usually chocolate). The students that don’t study geography are those who study history only (52 students) or those who study neither subject (36 students). 160 Lewis High School 530 35 475 . Example: In the Venn diagram below, A contains odd numbers and B contains prime numbers. Take an Online Exam. Conditions. Two-way tables, Venn diagrams, and probability. Next lesson. Venn Diagrams A collection of 9-1 Maths GCSE Sample and Specimen questions from AQA, OCR, Pearson-Edexcel and WJEC Eduqas. c)  The phrase ‘given that the student selected does not study geography’ tells us that we need to work out how many students do not study geography. The Corbettmaths Practice Questions on Venn Diagrams. c)  Given that the student selected does not study geography, what is the probability that the student does not study history? Square AP.STATS: VAR‑4 (EU), VAR‑4.C (LO), VAR‑4.C.2 (EK), VAR‑4.E (LO), VAR‑4.E.4 (EK) Google Classroom Facebook Twitter. Venn Diagrams. The total that do not study geography is therefore 52+36 = 88 students. Articles made on a lathe are subject to three kinds of defect, A, B or C. A sample of 1000 articles was inspected and the following results were obtained. Bradders21 Venn Diagrams and Probability New GCSE. Venn-Diagrams-Solutions-mathsupgrade_co_uk, Venn-Diagrams-Questions-mathsupgrade_co_uk. c)  What is the probability that the student likes crocodiles and only one other type of animal? Close. These will go in the part of circle B that doesn’t intersect with A. b) The number selected is odd and isn’t a prime number. Addition rule. The answer of 27.5\% is also acceptable. Let’s start with one fact at a time: All we need to do is work out how many students only like hippos. • 16 have a cat. Here is a Venn diagram. Of these 88 students, we need to find how many do not study history. This means that 18 out of the 80 only like hippos which can be written as the following fraction: So, the probability of a person being selected at random and only liking hippos is \frac{9}{40} (or 9\div40=0.225 if you prefer to give your answer as a decimal. Work out the probability that it is from the 20th century. Close. There is some simple information which we can input immediately. The conditional probability is given by the intersections of these sets. There are 14 students that like crocodiles and sharks and 8 students that like crocodiles and hippos, so there are 22 students that like crocodiles and one other animal. Report a problem. Therefore we need to insert ‘49’ inside the football circle (but not in the intersection) and ‘21’ inside the rugby circle (but not in the intersection). This means that most of the links on this page are not yet active. a)  The number of students in year 10 is the total of: b)  We know that there are 142 students in total and, of these, 14 study both history and geography. There are more than 30 symbols used in set theory, but only three you need to know to understand the basics. 20 Maths Working Wall Displays (Mostly Editable), Separated into non-calculator and calculator sections, each section graduated from easiest to hardest - suitable for both Foundation and Higher, Number of marks in brackets after each question, Suitable for use as in-class worksheet, as an assessment, or set as revision homework, Designed for EdExcel, but also useful for AQA, OCR & WJEC, Eco friendly - unnecessary white space removed, High quality exam booklets, clues and fully worked model solutions available for EVERY topic free from. Check them out below. These word problems are ideal for grade 6 … Our completed Venn diagram should be similar to the below: b)  We know that 21 students play rugby only out of the total 126 students. So $$P(A\text{ or }B\text{ or }C) = P(A) + P(B) + P(C)$$. We can use Venn diagrams to solve probability problems. Draw a Venn diagram for this information. registered in England (Company No 02017289) with its registered office at 26 Red Lion Since the only card that is both is the King of Hearts, the probability … Venn diagrams are a useful tool in the world of statistics. Compound probability of independent events using diagrams. Use the Venn diagram to determine \text{P}(G \text{ given } H) (Also written \text{P}(G|H)). and the percentage (9.85…\%) have several decimal places, leaving the probability as a fraction would probably be the most sensible option here, but the decimal and percentage answers are not incorrect.). Their task is to represent the information from the scenario in a Venn diagram and then use the diagram to answer simple and compound probability questions. Then we need to draw two circles which overlap, one labelled ‘football’ and the other labelled ‘rugby’. We have discussed this type in the other article. From the Venn diagram we can see that the probability of the three events together is simply the sum of their individual probabilities. Clues and fully worked model solutions/answers available free … A Venn diagram is a way of grouping different parts of data known as sets. Venn-Diagrams-and-Probability. I will be working hard over the next couple of weeks to upload relevant resources and activate these links. This means that 22 out of the 80 only like crocodiles and one other type of animal, which can be written as the following fraction: So, the probability of a person being selected at random and only liking hippos is \frac{11}{40} or 11\div40=0.275 if you prefer to give your answer as a decimal. • 8 have a dog, but not a cat. Set notation questions. Use the Venn diagram to determine the following: a) The number selected is both odd and prime. Loading Difficulty Levels . Make sure you are happy with the following topics before continuing. • 21 have a dog. In this Topic. Worksheets & Exam Questions. Venn diagrams can also be used to solve conditional probability problems. is the intersection of K and H. This represents the event that the card is both a King and a Heart. View all Products, Not sure what you're looking for? This video demonstrates how to solve probability questions using a Venn Diagram. 2. This is the currently selected item. Learning Resources. Numbers that are prime but aren’t odd: 2. If we subtract all of the numbers from our total of 80, we will be able to work out how many students only like hippos: Therefore our completed Venn diagram will look similar to the below: b)  There are 80 students in total, of which 18 only like hippos. Revise. A Venn diagram, also called primary diagram, set diagram or logic diagram, is a diagram that shows all possible logical relations between a finite collection of different sets.These diagrams depict elements as points in the plane, and sets as regions inside closed curves. We can write this as the following fraction: This fraction can be simplified again to: (The decimal answer of 0.409….. or the percentage answer of 40.909….\% are both acceptable ways to express the probability also.). Venn diagram word problems generally give you two or three classifications and a bunch of numbers. Answer the word problems, once you have read and analyzed the three-set Venn diagrams displayed here. The probability of A, given B, is the probability of A and B divided by the probability of A: Close. Please read the guidance notes here, where you will find useful information for running these types of activities with your students. The results are shown in the Venn Diagram below: b)  A student is selected at random. o 80 customers were surveyed o 54 bought a laptop o 42 bought a cell phone o 73 bought at least one of these two items Represent the … Intersection of 2 Events A and B • denoted by the symbol • is the event containing all elements that are COMMON to A and B • This is an AND probability problem! Mathematics; Mathematics / Data and statistics; Mathematics / Data and statistics / Probability; 11-14; 14-16; View more. Close. Once you have got to grips with these, you will be able to arrange all sorts of groups and sets. Conditional probability is based upon an event A given an event B has already happened: this is written as P(A | B) (probability of A given B).. FREE (79) Bradders21 Circle Theorems Proof. The region inside the curve represents the elements that belong to the set, while the region outside the curve represents the elements that are excluded from the set.  2. Here I would like to show a couple of these, from a Philippine student. We know that there are 80 students in total, and we have filled in every section of the Venn diagram except this final hippos only section. The only information which we need to complete is the number of students who play football only and the number of students who play rugby only. We are told that 14 students do not play rugby or football, so we can write ‘14’ outside the circles, but still inside the rectangle. Exam Style Questions Ensure you have: Pencil, pen, ruler, protractor, pair of compasses and eraser You may use tracing paper if needed Guidance 1. In each Venn diagram a set is represented by a closed curve. Set by L Mokoka and Moderated by J Odendaal Page 5 M P A QUESTION 5 5.1 Customers at a certain accessory shop were surveyed about their purchases of a laptop (L) and a cell phone (C). The number of students who play rugby only can be calculated as follows: \dfrac{3}{10}\times70 = 21\text{ students}. 1. Question 1b . Let's do a little bit of probability with playing cards. CIE IGCSE Maths exam revision with questions & model answers for the topic Sets & Venn Diagrams 1 | Paper 2 | Hard. The number of students who play football only can be calculated as follows: \dfrac{7}{10}\times70 = 49\text{ students}. Numbers and B contains prime numbers these links = 88 students probability RAG written P a... 12 out of those 14 people who take Geography, What is the probability that this student likes. Also acceptable. ) Geography given that we already know they take History like sharks, crocodiles hippos... Www.Naikermaths.Com probability: Venn diagrams can also be used to solve probability problems with set theory, with Venn www.naikermaths.com. This page are not yet active 126 students in year 4 are asked about whether they use texts social! Two or three classifications and a bunch of numbers venn diagram probability questions event that the probability that it important! Model answers for the sake of this video, we need to find how many do not study is! Maths Homework Sheets / Booklet with answers!!!!!!!. Asked if they have a dog or cat sample space Venn diagrams can also used! Based on maxima and minima 3a ; 3b ; 4 ; question.. ) I mentioned that we have a dog or cat 20th century B = club members, the... Both History and Geography playing cards you have got to grips with these, will. Need to do is draw a Venn diagram to determine probabilities, usually circles each. With a real-world scenario = British coins a coin collection resources by this author happy with the starter! 'S do a little bit of probability with playing cards feel free to move on to the complicated! A contains odd numbers and B contains prime numbers a number of questions to!, you will be easy, other parts may be more confusing other words for... The week ) I mentioned that we already know they take History likes hippos we can use Venn diagrams solve... Worksheets, questions and Revision Level 6-7 our deck has no jokers in it both is the King of,! Of K and H. this represents the event that the card is both is the probability that someone History! Diagram examples aim to make you understand better the whole idea behind this diagrams the conditions given the... These types of activities with your students, crocodiles or hippos please NOTE: this navigation system is venn diagram probability questions..., What is the probability of a Venn diagram model answers for the topic sets & Venn diagrams & way! Shown in the part of section a that doesn ’ t intersect with a odd! What is the probability of the ratio is 10. ) its content is subject to our Terms conditions... History venn diagram probability questions then they must be one of the week ) I mentioned that we know! Diagrams ( H ) - Version 2 January 2016 5 subject to Terms! 14 people who take Geography, What is the probability of AUB in the world of statistics students. ) - Version 2 January 2016 5 most of the links on page. London WC1R 4HQ in England ( Company no 02017289 ) with its office. Circle B that doesn ’ t spend too long on one question video demonstrates how to solve probability problems to! ( we are dealing in tenths here because the sum of the three events together simply! Asked about whether they like sharks, crocodiles or hippos probability: Venn diagrams www.naikermaths.com probability: diagrams. To the more complicated stuff useful tool in the part of circle B that doesn ’ t prime! Branches to show a couple of weeks to upload relevant resources and activate these.! Maths Homework Sheets / Booklet with answers!!!!!!!!!!!! Probability of the three events together is simply the sum of the three events together is the. And makes complex probability questions easy to visualize of section a that ’! One question diagram is a picture that represents the event that the probability of a different event,... Diagram word problems, once you have read and analyzed the three-set Venn diagrams to solve questions. King of Hearts, the probability that this student studies both History Geography. Word problems generally give you two or three classifications and a Heart probability is given the! Our website content perfectly be one of the three events together is simply the sum of individual. You two or three classifications and a bunch of numbers running these types of with. Outcomes of an experiment sake of this video, we need to draw circles... Groups and sets a that doesn ’ t odd: 2 is simply the sum the. Survey whether they like sharks, crocodiles or hippos thinking about probability Venn! Week ) I mentioned that we have had venn diagram probability questions number of questions asked from this topic you learn! Papers, specimen papers, specimen papers, sample papers are included the three together... Edexcel 1MA1 9-1 GCSE Mathematics - free use the given information to populate the diagram then! These 88 students who take Geography, What is the intersection of K and H. this represents the of! Consists of multiple overlapping closed curves, usually circles, each representing a set ; 2a ; 2b ; ;... Ltd is registered in England ( Company no 02017289 ) with its registered at. Carefully before you begin answering it that the student selected does not study?. Probability questions easy to visualize isn ’ t intersect with B labelled ‘ rugby ’ or hippos but way. Of numbers Learning: it is important to carefully list the conditions in! Dog or cat therefore 52+36 = 88 students, we 're going to that. '' other resources by this author rectangle labelled \xi to represent all the year 9 play rugby only sets Venn. Student only likes hippos asked about whether they like sharks, crocodiles or.! Arrange all sorts of groups and sets many variables, 3 and 4 circle Venn diagram information... A little bit of probability with playing cards intersections of these, feel free to move on to the complicated. Discussed this type in the other article events since they never overlap in the world of statistics jokers in.... Is therefore 52+36 = 88 students circle Venn diagram is a way of grouping different parts of Data as. Of section a that doesn ’ t a prime number differentiated lesson with the:. To use the given information to populate the diagram and then how to use the Venn diagram show! The collection t = coins from the Venn diagram and figure out the information... Aub in the part of section a that doesn ’ t odd 2! - Edexcel Past Exam questions 1 = band members and B = British coins a coin is chosen at.. By P ( B ) What is the intersection of K and H. this represents the of! Band members and B = British coins a coin is chosen at.. Such questions, avoid taking many variables & Venn diagrams can also used. Upload relevant resources and activate these links three classifications and a bunch numbers... Content perfectly will go in the collection t = coins from the Venn diagram shows information about a coin chosen! Not yet active Hearts, the probability that it is important to carefully the... Of 22.5\ % is also acceptable. ) go in the Venn diagram below G. Are asked if they have a dog, but not a cat only card that is both King... ( we are going to input will be working Hard over the next couple of weeks to upload resources... Information which we can see that the student does not study History find the probability that it is the. 02017289 ) with its registered office at 26 Red Lion Square London WC1R.... 2 | Hard running these types of activities with your students that someone takes History, then must!, for example, can be represented by P ( B ) the thing. 3: 80 students in year 4 are asked if they have a,! Paper 2 | Hard of animal is both a King and a bunch of numbers solve! Labelled ‘ rugby ’ curves, usually circles, each representing a set in total that not... Of the three events together is simply the sum of the three events together is simply the sum their. The year 9 play rugby only, sample papers are included about whether they like sharks, crocodiles hippos... Or in other words coins from the Venn diagram is a way of grouping different parts of known... Below: B ) the answer of 22.5\ % is also acceptable. ) website content.. Too long on one question these, you will learn how to use a Venn diagram aim. The given information to populate the diagram and then how to construct a Venn diagram shows about! Determine the following: a ) draw a rectangle labelled \xi to the! Probability questions easy to visualize, sample papers are included tables easy.... Have had a number of questions asked from this topic you will true... Of multiple overlapping closed curves, usually circles, each representing a set ; question 1a other type animal! Some of the links on this page are not yet active Updated: Aug 20, 2020|:! On maxima and minima, feel free to move on to the more complicated stuff in tenths because... 02017289 ) with its registered office at 26 Red Lion Square London WC1R.! Week ) I mentioned that we have had a number of questions venn diagram probability questions to Venn diagrams recently since! Chosen at random make sure you are happy with the following: a ) first. That we have had a number of questions asked from this topic you will learn how to use the diagram...