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

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

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

Page 1: 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?)

Page 2: Math-2 Lesson 10-3 Conditional 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.

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

Review of Probabilities

• Joint (overlapping) Probability

• Marginal (conditional) Probability

Page 4: Math-2 Lesson 10-3 Conditional Probability TB or not TB (did you get it?)

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

Page 5: Math-2 Lesson 10-3 Conditional Probability TB or not TB (did you get it?)

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

Page 6: Math-2 Lesson 10-3 Conditional Probability TB or not TB (did you get it?)

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

Page 7: Math-2 Lesson 10-3 Conditional Probability TB or not TB (did you get it?)

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

Page 8: Math-2 Lesson 10-3 Conditional Probability TB or not TB (did you get it?)

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

Page 9: Math-2 Lesson 10-3 Conditional Probability TB or not TB (did you get it?)

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

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

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

Page 11: Math-2 Lesson 10-3 Conditional Probability TB or not TB (did you get it?)

Writing Probability Statements

?

?)mammal / tail( P

?

?)mammalnot / tailno( P

?

?) tailno / mammal ( P

?

?) / tailmammalnot ( P

?

?)mammal( P

?

?)mammal anot ( P

Page 12: Math-2 Lesson 10-3 Conditional Probability TB or not TB (did you get it?)

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).

Page 13: Math-2 Lesson 10-3 Conditional Probability TB or not TB (did you get it?)

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.

Page 14: Math-2 Lesson 10-3 Conditional Probability TB or not TB (did you get it?)

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

Page 15: Math-2 Lesson 10-3 Conditional Probability TB or not TB (did you get it?)

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

Page 16: Math-2 Lesson 10-3 Conditional Probability TB or not TB (did you get it?)

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

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Page 17: Math-2 Lesson 10-3 Conditional Probability TB or not TB (did you get it?)

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.

Page 18: Math-2 Lesson 10-3 Conditional Probability TB or not TB (did you get it?)

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:

Page 19: Math-2 Lesson 10-3 Conditional Probability TB or not TB (did you get it?)

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

Page 20: Math-2 Lesson 10-3 Conditional Probability TB or not TB (did you get it?)

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

Page 21: Math-2 Lesson 10-3 Conditional Probability TB or not TB (did you get it?)

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

Page 22: Math-2 Lesson 10-3 Conditional Probability TB or not TB (did you get it?)

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

Page 23: Math-2 Lesson 10-3 Conditional Probability TB or not TB (did you get it?)

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

Page 24: Math-2 Lesson 10-3 Conditional Probability TB or not TB (did you get it?)

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

Page 25: Math-2 Lesson 10-3 Conditional Probability TB or not TB (did you get it?)

Homework 10.3

• Finish the TB Activity• Part 1: Fill in table, Questions 1-2• Part 2: Questions 1-7