1. Math-2 Lesson 10-3 Conditional Probability TB or not TB (did you get it?)

2. Marginal and Conditional Probability Marginal probability: the probability of an event occurring (p(A)), it may be thought of as an unconditional probability. It is not conditioned on another event. – Example: the probability that a card drawn is red (p(red) = 0.5). Another example: the probability that a card drawn is a 4 (p(four)=1/13). Conditional probability: p(A|B) is the probability of event A occurring, given that event B occurs. – Example: given that you drew a red card, what’s the probability that it’s a four (p(four|red))=2/26=1/13. So out of the 26 red cards (given a red card), there are two fours so 2/26=1/13.

3. Review of Probabilities Joint (overlapping) Probability Marginal (conditional) Probability

4. 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)

5. Marginal (conditional) Probability FordNon-Fordtotal white Not white total 2 4 7 0 6 4 13 9 7

6. Joint (overlapping) and Marginal (conditional) Probabilities FordNon-Fordtotal white Not white total 2 4 7 0 6 4 13 9 7

7. Probability Statements

8. Tree Diagram Steeler Games: 16 49er Games: 16 Won/Steeler: 7 Lost/Steeler: 8 Lost/49er: 6 Won/49er: 10 WinsLossesTie GamesTotal Steelers78116 49ers106016 Total1714132 Games: 32 tie/Steeler: 1 tie/49er: 0

9. Steeler Games: 16 49er Games: 16 Won/Steeler: 7 Lost/Steeler: 8 Lost/49er: 6 Won/49er: 10 Games: 32 tie/Steeler: 1 What did you notice about how fare “upstream” you go to find numbers for the “marginal” probabilities?

10. Your turn: Mammals: 9 Not mammals: 10 Tails/mammal: 5 no tails/mammal: 4 No tails/not mammal: 3 Tails/not mammal: 7 TailsNo tailsTotal Mammals54 Not mammals73 Total Animals 19: 1. 1. Fill in the table. 2. 2. Build a tree diagram and label it. 127 9 10 19

11. Writing Probability Statements

12. Fords: Chevy’s: Blue/Ford: Not blue/Ford: Not Blue/Chevy: Blue/Chevy BlueNot BlueTotal Ford Chevy Total Cars: Build a tree diagram and label it (without #’s at first).

13. Fords: Chevy’s: Blue/Ford: Not blue/Ford: Not Blue/Chevy: Blue/Chevy BlueNot BlueTotal Ford Chevy Total Cars: From the probability given, fill in the table or the tree. 27 15 27 – 15 = 12 27 15 This probability gives you 2 numbers in the table/tree. 12 From these 2 numbers you can find a 3 rd number.

14. Fords: Chevy’s: Blue/Ford: Not blue/Ford: Not Blue/Chevy: Blue/Chevy BlueNot BlueTotal Ford Chevy Total Cars: From the probability given, fill in the table or the tree. 43 27 43 - 27 = 16 43 1512 11 This probability gives you 2 numbers in the table/tree. 27 15 12 You now have enough information to complete the table and the tree. 16

15. Fords: Chevy’s: Blue/Ford: Not blue/Ford: Not Blue/Chevy: Blue/Chevy BlueNot BlueTotal Ford Chevy Total Cars: From the probability given, fill in the table or the tree. 43 27 16 43 1512 11 This probability gives you 2 numbers in the table/tree. 27 15 12 You now have enough information to complete the table and the tree. 16 – 11 = 5 5 16

16. Fords: Chevy’s: Blue/Ford: Not blue/Ford: Not Blue/Chevy: Blue/Chevy BlueNot BlueTotal Ford Chevy Total Cars: From the probability given, fill in the table or the tree. 15 + 11 = 26 43 27 16 43 1512 11 This probability gives you 2 numbers in the table/tree. 27 15 12 You now have enough information to complete the table and the tree. 5 5 16

17. 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.

18. Test Positive: Test Negative: Have TB/”+” test: Don’t have TB/ “+”test: Test PositiveTest NegativeTotal Have TB Don’t have TB Total Patients: Build a tree diagram and label it. Have TB/ ”neg” test: Don’t have TB/ “neg”test:

19. Test Positive: Test Negative: Have TB/”+” test: Don’t have TB/ “+”test: Test PositiveTest NegativeTotal Have TB Don’t have TB Total Patients: From the probability given, fill in the table and the tree. 725 675 Have TB/ ”neg” test: Don’t have TB/ “neg”test: 725 675 This probability gives you 2 numbers in the table/tree. From these 2 numbers you can find a 3 rd number. 725 – 675 = 50 50

20. Test Positive: Test Negative: Have TB/”+” test: Don’t have TB/ “+”test: Test PositiveTest NegativeTotal Have TB Don’t have TB Total Patients: From the probability given, fill in the table and the tree. 725 675 Have TB/ ”neg” test: Don’t have TB/ “neg”test: 725 675 This probability gives you 2 numbers in the table/tree. This provides enough information to file in the rest of the table/tree. 50 1015 830 1015 1015 – 830 = 185 50

21. Test Positive: Test Negative: Have TB/”+” test: Don’t have TB/ “+”test: Test PositiveTest NegativeTotal Have TB Don’t have TB Total Patients: From the probability given, fill in the table and the tree. 725 675 Have TB/ ”neg” test: Don’t have TB/ “neg”test: 725 675 This probability gives you 2 numbers in the table/tree. This provides enough information to file in the rest of the table/tree. 50 1015 830 1015 185 155 830 – 675 = 155 50

22. Test Positive: Test Negative: Have TB/”+” test: Don’t have TB/ “+”test: Test PositiveTest NegativeTotal Have TB Don’t have TB Total Patients: From the probability given, fill in the table and the tree. 725 675 Have TB/ ”neg” test: Don’t have TB/ “neg”test: 725 675 This probability gives you 2 numbers in the table/tree. This provides enough information to file in the rest of the table/tree. 50 1015 830 1015 185 155 1015 – 725 = 290 290 155 50

23. Test Positive: Test Negative: Have TB/”+” test: Don’t have TB/ “+”test: Test PositiveTest NegativeTotal Have TB Don’t have TB Total Patients: From the probability given, fill in the table and the tree. 725 675 Have TB/ ”neg” test: Don’t have TB/ “neg”test: 725 675 This probability gives you 2 numbers in the table/tree. This provides enough information to file in the rest of the table/tree. 50 1015 830 1015 185 155 290 290 – 155 = 135 155 135 50

24. 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

25. Homework 10.3 Finish the TB Activity Part 1: Fill in table, Questions 1-2 Part 2: Questions 1-7