Math-2 Lesson 10-3 Conditional Probability TB or not TB (did you get it?)
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Transcript of Math-2 Lesson 10-3 Conditional Probability TB or not TB (did you get it?)
Math-2
Lesson 10-3Conditional Probability
TB or not TB (did you get it?)
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.
Review of Probabilities
• Joint (overlapping) Probability
• Marginal (conditional) Probability
Joint Probability (overlapping events).
BlondeHair(3)
Girls (3)Bill Jim Amber
MariaAngelica
(2)(1) (2)
Not girl,blonde
(2)
Girl, blonde(1)
Girl, not blonde
(2)
?
?)girl blonde( P
?
?)boy blonde( P
Marginal (conditional) Probability
Ford Non-Ford total
white
Not white
total
2
4
7
0
6
4
13
9
7
?
?)Fordwhite( P
?
?)Ford-notwhite( P
?
?)Fordwhite-not( P
?
?)Ford-notwhite-not( P
Joint (overlapping) andMarginal (conditional) Probabilities
Ford Non-Ford total
white
Not white
total
2
4
7
06
4
13
9
7
?
?)Ford and white( P
?
?)Ford / white-not( P
?
?)Ford and white-not( P
?
?) / whiteFord-not( P
Probability Statements
13
2)Ford and white( P
3
2)Ford| white-not( P
13
4)Ford and white-not( P
9
7)white| Ford-not( P
Tree Diagram
Steeler Games: 16
49erGames: 16
Won/Steeler: 7
Lost/Steeler: 8
Lost/49er: 6
Won/49er: 10
Wins Losses Tie Games Total
Steelers 7 8 1 16
49ers 10 6 0 16
Total 17 14 1 32
Games: 32tie/Steeler: 1
tie/49er: 0
Steeler Games: 16
49erGames: 16
Won/Steeler: 7
Lost/Steeler: 8
Lost/49er: 6
Won/49er: 10
Games: 32tie/Steeler: 1
tie/Steeler: 1
?
?)game 94/( winP
What did you notice about how fare “upstream” you go to find numbers for the “marginal” probabilities?
16
10
Your turn:
Mammals: 9
Not mammals: 10
Tails/mammal: 5
no tails/mammal: 4
No tails/not mammal: 3
Tails/not mammal: 7
Tails No tails Total
Mammals 5 4
Not mammals 7 3
Total
Animals 19:
1. Fill in the table.2. Build a tree diagram and label it.
12 7
9
1019
Writing Probability Statements
?
?)mammal / tail( P
?
?)mammalnot / tailno( P
?
?) tailno / mammal ( P
?
?) / tailmammalnot ( P
?
?)mammal( P
?
?)mammal anot ( P
Fords:
Chevy’s:
Blue/Ford:
Not blue/Ford:
Not Blue/Chevy:
Blue/Chevy
Blue Not Blue Total
Ford
Chevy
Total
Cars:
Build a tree diagram and label it (without #’s at first).
Fords:
Chevy’s:
Blue/Ford:
Not blue/Ford:
Not Blue/Chevy:
Blue/Chevy
Blue Not Blue Total
Ford
Chevy
Total
Cars:
From the probability given, fill in the table or the tree.
27
27
15)car/Ford Blue( P
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 3rd number.
Fords:
Chevy’s:
Blue/Ford:
Not blue/Ford:
Not Blue/Chevy:
Blue/Chevy
Blue Not Blue Total
Ford
Chevy
Total
Cars:
From the probability given, fill in the table or the tree.
43
27
43 - 27 = 1643
43
11)Chevy and Blue( P
15 12
11
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
Fords:
Chevy’s:
Blue/Ford:
Not blue/Ford:
Not Blue/Chevy:
Blue/Chevy
Blue Not Blue Total
Ford
Chevy
Total
Cars:
From the probability given, fill in the table or the tree.
43
2716
43
43
11)Chevy and Blue( P
15 12
11
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
Fords:
Chevy’s:
Blue/Ford:
Not blue/Ford:
Not Blue/Chevy:
Blue/Chevy
Blue Not Blue Total
Ford
Chevy
Total
Cars:
From the probability given, fill in the table or the tree.
15 + 11 = 26
43
2716
43
43
11)Chevy and Blue( P
15 12
11
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
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.
Test Positive:
Test Negative:
Have TB/”+” test:
Don’t have TB/ “+”test:
Test Positive Test Negative Total
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:
Test Positive:
Test Negative:
Have TB/”+” test:
Don’t have TB/ “+”test:
Test Positive Test Negative Total
Have TB
Don’t have TB
Total
Patients:
From the probability given, fill in the table and the tree.
725
725
675) test"/"T( BP
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 3rd number.
725 – 675 = 50
50
Test Positive:
Test Negative:
Have TB/”+” test:
Don’t have TB/ “+”test:
Test Positive Test Negative Total
Have TB
Don’t have TB
Total
Patients:
From the probability given, fill in the table and the tree.
725
1015
830)T( BP
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
Test Positive:
Test Negative:
Have TB/”+” test:
Don’t have TB/ “+”test:
Test Positive Test Negative Total
Have TB
Don’t have TB
Total
Patients:
From the probability given, fill in the table and the tree.
725
1015
830)T( BP
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
Test Positive:
Test Negative:
Have TB/”+” test:
Don’t have TB/ “+”test:
Test Positive Test Negative Total
Have TB
Don’t have TB
Total
Patients:
From the probability given, fill in the table and the tree.
725
1015
830)T( BP
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
Test Positive:
Test Negative:
Have TB/”+” test:
Don’t have TB/ “+”test:
Test Positive Test Negative Total
Have TB
Don’t have TB
Total
Patients:
From the probability given, fill in the table and the tree.
725
1015
830)T( BP
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
290 – 155 = 135155
135
50
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 NOTHave TB: 620
Tested Positive/yes TB: 361
Tested Negative/ yes TB 19
Tested Negative/no TB: 553
Tested Positive/no TB: 62
# tested: 1000
Homework 10.3
• Finish the TB Activity• Part 1: Fill in table, Questions 1-2• Part 2: Questions 1-7