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

2. Joint and Conditional Probabilities
Joint Probability:  p(A and B).  The probability of event A and event B occurring.  It is the probability of the intersection of two or more events.  The probability of the intersection of A and B may be written p(A ∩ B).
Example:  the probability that a card is a four and red =p(four and red) = 2/52 = 1/26.   (There are two red fours in a deck of 52, the 4 of hearts and the 4 of diamonds).
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 – and (∩)
Conditional Probability – (|)

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

5. Conditional Probability
Ford
Non-Ford
total
white
Not white 7 2 9 4 4 6 7 13
1/9, 2/3,7/9, 0

6. Joint (overlapping) and Conditional Probabilities
Ford
Non-Ford
total
white
Not white 7 2 9 4 4 6 7 13

7. Probability Statements

8. Tree Diagram Wins Losses Tie Games Total Steelers 7 8 1 16 49ers 10 617 14 32
Won/Steeler: 7
Steeler
Games: 16
Lost/Steeler: 8
Games: 32
tie/Steeler: 1
Won/49er: 10
49er
Games: 16
Lost/49er: 6
tie/49er: 0

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

10. Your turn: 1. Fill in the table. 2. Build a tree diagram and label it.
Tails
No tails
Total
Mammals 5 4
Not mammals 7 3 9 10 12 7 19
Tails/mammal: 5
Mammals: 9
Animals 19:
no tails/mammal: 4
Tails/not mammal: 7
Not mammals: 10
No tails/not mammal: 3

11. Writing Probability Statements

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

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

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

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

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

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

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

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

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

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

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

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

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