Reverse conditional probability with a tree (tests and filters)
11th grade (Year 12 in England) · 16 questions · Common Core: HSS.CP.A.3, HSS.CP.B.6 · England: A-level Statistics
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Question 1
20% of emails are spam. A filter flags 90% of spam emails and 5% of genuine emails. An email is flagged. What is the probability it is spam? Give 3 decimal places.
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Question 2
10% of people have a condition. A test is positive for 95% of people who have it and for 5% of people who don't. Someone tests positive. What is the probability they have the condition? Give 3 decimal places.
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Question 3
20% of emails are spam. A filter flags 90% of spam emails and 10% of genuine emails. An email is flagged. What is the probability it is spam? Give 3 decimal places.
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Question 4
2% of people have a condition. A test is positive for 99% of people who have it and for 10% of people who don't. Someone tests positive. What is the probability they have the condition? Give 3 decimal places.
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Question 5
30% of emails are spam. A filter flags 90% of spam emails and 5% of genuine emails. An email is flagged. What is the probability it is spam? Give 3 decimal places.
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Question 6
5% of people have a condition. A test is positive for 90% of people who have it and for 5% of people who don't. Someone tests positive. What is the probability they have the condition? Give 3 decimal places.
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Question 7
30% of emails are spam. A filter flags 90% of spam emails and 10% of genuine emails. An email is flagged. What is the probability it is spam? Give 3 decimal places.
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Question 8
1% of people have a condition. A test is positive for 99% of people who have it and for 10% of people who don't. Someone tests positive. What is the probability they have the condition? Give 3 decimal places.
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Question 9
20% of emails are spam. A filter flags 80% of spam emails and 10% of genuine emails. An email is flagged. What is the probability it is spam? Give 3 decimal places.
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Question 10
2% of people have a condition. A test is positive for 99% of people who have it and for 10% of people who don't. Someone tests positive. What is the probability they have the condition? Give 3 decimal places.
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Question 11
20% of emails are spam. A filter flags 80% of spam emails and 10% of genuine emails. An email is flagged. What is the probability it is spam? Give 3 decimal places.
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Question 12
5% of people have a condition. A test is positive for 99% of people who have it and for 10% of people who don't. Someone tests positive. What is the probability they have the condition? Give 3 decimal places.
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Question 13
20% of emails are spam. A filter flags 90% of spam emails and 10% of genuine emails. An email is flagged. What is the probability it is spam? Give 3 decimal places.
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Question 14
1% of people have a condition. A test is positive for 99% of people who have it and for 2% of people who don't. Someone tests positive. What is the probability they have the condition? Give 3 decimal places.
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Question 15
30% of emails are spam. A filter flags 90% of spam emails and 5% of genuine emails. An email is flagged. What is the probability it is spam? Give 3 decimal places.
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Question 16
10% of people have a condition. A test is positive for 90% of people who have it and for 10% of people who don't. Someone tests positive. What is the probability they have the condition? Give 3 decimal places.
Answer
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