Probability and Two-Way Tables Practice Examples

Explore various probability scenarios through Venn diagrams and two-way tables in this practice session. Calculate probabilities of students liking specific sports and subjects, and determine conditional probabilities based on given conditions. Enhance your understanding of probability concepts with worked examples and practice questions.

• Probability
• Venn diagrams
• Two-way tables
• Practice
• Conditional probability

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Uploaded on Jul 19, 2024 | 0 Views

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Presentation Transcript

1. Probability: Venn Diagrams and Probability: Venn Diagrams and Two Two- -Way Tables Way Tables Silent Teacher Intelligent Practice Your Turn Narration Practice

2. Worked Example Your Turn Football Football Tennis Tennis 3 1 5 2 4 2 5 3 4 6 3 5 14 4 15 4 Rugby Rugby 40 people are surveyed about their favourite sports and the results are shown in the Venn diagram above. 1) Find the probability of a student liking tennis and rugby 40 people are surveyed about their favourite sports and the results are shown in the Venn diagram above. 1) Find the probability of a student liking tennis and rugby 2) Find the probability of a student liking tennis or rugby 2) Find the probability of a student liking tennis or rugby 3) Given that a student likes tennis, what is the probability they like football 3) Given that a student likes tennis, what is the probability they like football 4) Given that a student likes tennis, what is the probability that they like rugby 4) Given that a student likes tennis, what is the probability that they like rugby

3. Worked Example Your Turn The two-way table below shows the subjects 120 students The two-way table below shows the subjects 120 students Left handed Right handed Total Left handed Right handed Total French 25 35 60 French 20 40 60 Spanish 12 48 60 Spanish 18 42 60 Total 37 83 120 Total 38 82 120 1) Find the probability of a student taking French or Spanish 1) Find the probability of a student taking French or Spanish 2) Find the probability of a student taking French and Spanish 2) Find the probability of a student taking French and is right handed 3) Given that a student is right handed, what is the probability they take French? 3) Given that a student is right handed, what is the probability they take French? 4) Given that a student is right handed, what is the probability they take Spanish? 4) Given that a student is right handed, what is the probability they take Spanish?

4. The two-way table below shows the subjects of 80 students French Spanish Left handed Right handed Total 1 4 2 French 18 26 44 3 6 5 Spanish 9 27 36 15 4 Total 27 53 80 Latin 1) Find the probability of a student taking French 1) Find the probability of a student taking French 2) Find the probability of a student taking French or Spanish 2) Find the probability of a student taking French or Spanish 3) Find the probability of a student taking French and Spanish 3) Given that a student is right handed, what is the probability they take French? 4) Given that a student takes Spanish, what is the probability they take Latin? 4) Given that a student is right handed, what is the probability they take Spanish? 5) What is the probability that a student takes Latin given that they take Spanish? 5) Given that a student is left handed, what is the probability they take Spanish? 6) What is the probability that a student does not take French given that they take Latin? 6) Given that a student is left handed, what is the probability they are right handed?

5. The two-way table below shows the subjects of 110 students Geography History Left handed Right handed Total 7 4 3 Geography 60 26 86 5 0 11 History 5 19 24 15 5 Total 65 45 110 Business 1) Find the probability of a student taking Business 1) Find the probability of a student taking History 2) Find the probability of a student taking Business or History 2) Find the probability of a student taking History or Geography 3) Find the probability of a student taking Business and History 3) Given that a student is right handed, what is the probability they take History? 4) Given that a student takes Geography, what is the probability they take History? 4) Given that a student is right handed, what is the probability they take Geography? 5) What is the probability that a student takes History given that they take Geography? 5) Given that a student is left handed, what is the probability they take Geography? 6) What is the probability that a student does not take Business given that they take History? 6) Given that a student is left handed, what is the probability they do not take Geography?

6. The two-way table below shows the subjects of 80 students French Spanish Left handed Right handed Total 1 4 2 French 18 26 44 3 6 5 Spanish 9 27 36 15 4 11 40 Total 27 53 80 Latin 44 80 1) Find the probability of a student taking French 1) Find the probability of a student taking French 2) Find the probability of a student taking French or Spanish 80= 1 2) Find the probability of a student taking French or Spanish 21 40 80 3) Find the probability of a student taking French and Spanish 3) Given that a student is right handed, what is the probability they take French? 26 53 5 40 4) Given that a student takes Spanish, what is the probability they take Latin? 4) Given that a student is right handed, what is the probability they take Spanish? 9 27 53 9 27 0 15 5) What is the probability that a student takes Latin given that they take Spanish? 5) Given that a student is left handed, what is the probability they take Spanish? 9 6 15 6) What is the probability that a student does not take French given that they take Latin? 6) Given that a student is left handed, what is the probability they are right handed? 29

7. The two-way table below shows the subjects of 110 students Geography History Left handed Right handed Total 7 4 3 Geography 60 26 86 5 0 11 History 5 19 24 15 5 31 50 Total 65 45 110 Business 24 110 1) Find the probability of a student taking Business 1) Find the probability of a student taking History 2) Find the probability of a student taking Business or History 38 50 2) Find the probability of a student taking History or Geography 110 110= 1 3) Find the probability of a student taking Business and History 5 50 3) Given that a student is right handed, what is the probability they take History? 19 45 4) Given that a student takes Geography, what is the probability they take History? 4) Given that a student is right handed, what is the probability they take Geography? 8 26 45 26 8 5) What is the probability that a student takes History given that they take Geography? 5) Given that a student is left handed, what is the probability they take Geography? 60 65 26 3 12 5 6) What is the probability that a student does not take Business given that they take History? 6) Given that a student is left handed, what is the probability they do not take Geography? 65