Probability Venn Diagrams Which burger would you choose
Probability Venn Diagrams
Which burger would you choose? Bacon Cheese £ 9 £ 8. 50 £ 7 £ 10 £ 8 £ 9. 50 £ 7. 50 Onion Rings
Sorting Data Using Venn Diagrams Sort the numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 Square number Triangular number
Sorting Data Using Venn Diagrams Sort the numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 Square number Triangular number 2 5 3 1 4 7 8 9 10 6
Solving Problems Using Venn Diagrams 1. 40 people were asked if they prefer butter, mayonnaise or both on their sandwiches. 29 take butter and 14 take mayonnaise. If 5 people take both, how many take: (i) Only butter? (ii) Only mayonnaise? (iii) Neither? What is the probability that a person chosen at random from the group will take butter but not mayonnaise?
Solution a) (i) 5 people take both so 29 - 5 = 24 take butter only. (ii) 14 - 5 = 9 take mayonnaise only. (iii) This leaves 40 - 24 - 5 - 9 = 2 who take neither. Butter Mayonnaise 2 24 5 9
A Probability Problem 2. The probability a male teacher has a beard is 0. 4. The probability a male teacher has glasses is 0. 5. The probability a male teacher does not have glasses or a beard is 0. 3. Use a Venn diagram to work out the probability of a male teacher selected at random has a beard and glasses.
Solution ● As the probabilities must add up to 1 we can work out what the intersection must be. ● 0. 4 + 0. 5 + 0. 3 = 1. 2 The intersection must be 0. 2 ● Using this information we can complete the Venn diagram. ● P(Beard and Glases) = 0. 2 Beard Glasses 0. 2 0. 3 0. 2
3 Circle problems In a class of 30 students all students study either Science, Geography or History: 1 student studies Geography, Science and History 3 students study Science and Geography 7 students study Science and History 6 students study Geography and History 17 students study Science 13 students study Geography 15 students study History Complete a Venn diagram for the students
When dealing with this type of problem make sure to start in the middle and work your way out. Don’t forget to subtract the number doing all 3 from the number doing Science and Geography. Science Geography 2 8 5 1 6 5 3 History
Calculating Probabilities including ‘given that’ Use the Venn diagram on the previous slide to answer the following questions: a) What is the probability that a student selected at random will study: (i) Geography? 13/30 (ii) Science, Geography or both but not History? 15/30 b) Given that a student studies Geography, what is the probability they also study History? 6/13
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