Math-3 Lesson 1-2: TB or not TB (did you get it?).

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Presentation transcript:

Math-3 Lesson 1-2: TB or not TB (did you get it?)

Joint Probability (overlapping events). Blonde Hair (3) Girls (3) Bill Jim Amber Maria Angelica (2) (1) (2) Not girl, blonde (2) Girl, blonde (1) Girl, not blonde (2)

Joint (overlapping) and Marginal (conditional) Probabilities FordNon-Fordtotal white Not white total

Probability Statements

Tree Diagram Steeler Games: 16 49er Games: 16 Won/Steeler: 7 Lost/Steeler: 8 Lost/49er: 6 Won/49er: 10 WinsLossesTie GamesTotal Steelers ers Total Games: 32 tie/Steeler: 1

Your turn: Mammals: 9 Not mammals: 10 mammals/tails: 5 Mammals/no tails: 4 Not mammals/no tails: 3 Not mammal/tails: 7 TailsNo tailsTotal Mammals54 Not mammals73 Total Animals 19: Fill in the table Build a tree diagram and label it

Writing Probability Statements

TB or Not TB? Tuberculosis (TB) can be tested in a variety of ways, including a skin test. If a person has tuberculosis antibodies, then they are considered to have TB.

Below is a tree diagram representing data based on 1,000 people who have been given a skin test for tuberculosis. Have TB: 380 Do NOT Have TB: 620 Tested Positive/yes TB: 361 Tested Negative/ yes TB 19 Tested Negative/no TB: 553 Tested Positive/no TB: 62 # tested: 1000

Your turn: 1. Use your knowledge to write several probability statements about this test (based on the numbers provided). 2. Look over the statements you wrote. Put an asterisk (*) next to those that are conditional probability statements (statements based on margin “row” or “column” percentages). If you didn’t write any (in #1 above), add some now.

Your turn: 3. Part of understanding the world around us is being able to take information, make sense of it, and then explain it to others. Based on your statements above, write down what you would say to a friend regarding the validity of their results if they are testing for TB and only get a skin test? Be sure to use data to best inform your friend.

4. In this situation, explain the consequences of errors (having a test with incorrect results). 5. If a health test is not 100% certain, why might it be beneficial to have the results lean more toward a false positive? 6. Is a sample space of 200 enough to indicate whether or not this is true for an entire population? 7. How would you answer the young adult who tested positive and asks, “Do I really have TB?”

10. What does the number 375 represent? 11. How many students are in both choir and band? 12. How many students are not in either choir or band? 13. What is the probability that a randomly selected student would be in band? 8. How many students were surveyed? 9. What were the students asked?

15. How many total students are represented in the diagram? 17. Which elective class has the least number of students enrolled? 14. What does the 95 in the center tell you? 15. What does the 145 tell you?

19. Based on this data, if you are a left-‐handed hitter what is the probability that you will face a right—handed pitcher? 20. Based on this data, if you are a right– handed hitter what is the probability that you will face a left—handed pitcher? 18. How many times did a batter come to the plate during this time period?

13. What is the probability that a left—handed pitcher will be throwing for any given plate appearance? 14. What is the probability that a left-handed hitter would be at the plate for any given plate appearance? 14. What observations do you make about the data? 15. Is there any amount that seems to be overly abundant? 16. What might account for this?

Find the probability of achieving success with each of the following events: 17. Rolling an even number on a standard six-sided die. 18. Drawing a black card from a standard deck of playing cards. 19. Rolling a die and getting a four. 20. Drawing an Ace from a deck of playing cards. 21. From a bag containing 3 blue, 2 red, and 5 white marbles, pulling out a red marble.