A great prize is inside Box 1, 2, or 3. You choose Box 1. You are shown that Box 2 contains a rubber...

10
* Conditional Probability

Transcript of A great prize is inside Box 1, 2, or 3. You choose Box 1. You are shown that Box 2 contains a rubber...

Page 1: A great prize is inside Box 1, 2, or 3. You choose Box 1. You are shown that Box 2 contains a rubber chicken. You are given a chance to change your choice.

*Conditional Probability

Page 2: A great prize is inside Box 1, 2, or 3. You choose Box 1. You are shown that Box 2 contains a rubber chicken. You are given a chance to change your choice.

Think about it

A great prize is inside Box 1, 2, or 3. You choose Box 1. You are shown that Box 2 contains a rubber chicken. You are given a chance to change your choice. Should you stay with Box 1 or should you change to Box 3? Justify your answer.

Page 3: A great prize is inside Box 1, 2, or 3. You choose Box 1. You are shown that Box 2 contains a rubber chicken. You are given a chance to change your choice.

*The probability that an event, B, will occur given that another event, A, has already occurred is called a conditional probability.

Write: )

Read: the probability of event B, given

event A.

Page 4: A great prize is inside Box 1, 2, or 3. You choose Box 1. You are shown that Box 2 contains a rubber chicken. You are given a chance to change your choice.

Formula

For any two events A and B with

)

Page 5: A great prize is inside Box 1, 2, or 3. You choose Box 1. You are shown that Box 2 contains a rubber chicken. You are given a chance to change your choice.

*Example

Males (in thousands)

Females(in thousands)

Two year colleges

1866 2462

Four year colleges

4324 5517

Grad School 1349 1954What is P(female/graduate school)?

What is P(female)?

What is P(four year/male)?

Page 6: A great prize is inside Box 1, 2, or 3. You choose Box 1. You are shown that Box 2 contains a rubber chicken. You are given a chance to change your choice.

Material Recycled Not Recycled

Paper 45.2 37.8

Metal 7.2 13.6

Glass 3.2 10.4

Plastic 2.1 28.6

Other 21.7 46.3What is the probability that a sample of recycled waste is paper?

What is the probability that a sample of recycled wasted is plastic?

What is the probability that a sample of recycled waste is glass?

Municipal Waste Collected(millions of tons)

Page 7: A great prize is inside Box 1, 2, or 3. You choose Box 1. You are shown that Box 2 contains a rubber chicken. You are given a chance to change your choice.

*Example

Bill Payment

Online By Mail

Male 12 8

Female 24 6

A utility company asked 50 of its customers whether they pay their bills online or by mail. What is the probability that a customer pays the bill online, given that the customer is male?

Page 8: A great prize is inside Box 1, 2, or 3. You choose Box 1. You are shown that Box 2 contains a rubber chicken. You are given a chance to change your choice.

*Example

Applying Shampoo

Directly to head

Into hand first

Male 2 18

Female 6 24

Researchers asked shampoo users whether they apply shampoo directly to the head, or indirectly using a hand. What is the probability that a respondent applies shampoo directly to the head, given that the respondent is female?

Page 9: A great prize is inside Box 1, 2, or 3. You choose Box 1. You are shown that Box 2 contains a rubber chicken. You are given a chance to change your choice.

It follows from ) that

Page 10: A great prize is inside Box 1, 2, or 3. You choose Box 1. You are shown that Box 2 contains a rubber chicken. You are given a chance to change your choice.

Make a Tree Diagram

A school system compiled the following information from a survey it sent to people who were juniors 10 years earlier.

*85% of the students graduated

*Of those that graduated, 90% were happy with their present job

*Of those who did not graduate, 60% were happy with their present job.

What is the probability that a person from the junior class 10 years ago graduated from high school and is happy with their present job?


Prize Incentive Program...Prize Incentive Program 6/25/2017 4 Council Flyer & Tally Sheet: Here you can find your Council’s Prize Incentive Flyer for prize options available to your

Prize Incentive Program...Prize Incentive Program 6/25/2017 4 Council Flyer & Tally Sheet: Here you can find your Council’s Prize Incentive Flyer for prize options available to your

HALIMA - Bait Al Arab · sAAd AHMEd ALFArHAn HAssAn AL-dAsHTI ZAInAb MurTAdHAWI 1. prize 2. prize 3. prize 4. prize 5. prize 6. prize 7. prize 8. prize 9. prize 10. prize From left

HALIMA - Bait Al Arab · sAAd AHMEd ALFArHAn HAssAn AL-dAsHTI ZAInAb MurTAdHAWI 1. prize 2. prize 3. prize 4. prize 5. prize 6. prize 7. prize 8. prize 9. prize 10. prize From left

Because winning a Spike seems an elusive prize, you can ......Because winning a Spike seems an elusive prize, you can begin to believe that, behind the scenes of the work that does

Because winning a Spike seems an elusive prize, you can ......Because winning a Spike seems an elusive prize, you can begin to believe that, behind the scenes of the work that does

Set-Top Box Capable of Real-Time Video Processing Box Capable of Real-Time Video Processing 51 Second Prize Set-Top Box Capable of Real-Time Video Processing Institution: Xi’an University

Set-Top Box Capable of Real-Time Video Processing Box Capable of Real-Time Video Processing 51 Second Prize Set-Top Box Capable of Real-Time Video Processing Institution: Xi’an University

Black Box Lush Prize 2015: Skin Sensitization Adverse Outcome Pathway G. Frank Gerberick The Procter & Gamble Company.

Black Box Lush Prize 2015: Skin Sensitization Adverse Outcome Pathway G. Frank Gerberick The Procter & Gamble Company.

Signagesolution · Art Workshop comences in Painting Competition Results 1 st Prize 2nd Prize 3rd Prize Discovering the professional in you. Universiþy, LIVE Stellar Academy of ...

Signagesolution · Art Workshop comences in Painting Competition Results 1 st Prize 2nd Prize 3rd Prize Discovering the professional in you. Universiþy, LIVE Stellar Academy of ...

Box. Box Enterprise Box @KU Leuven –What? –Why? –How? Box Essentials Webapp –Finding what you need –Adding content –Creating content (Box Edit) –Versioning.

Box. Box Enterprise Box @KU Leuven –What? –Why? –How? Box Essentials Webapp –Finding what you need –Adding content –Creating content (Box Edit) –Versioning.

yappusa.com · Spammers often send emails claiming that you have won a sweepstakes or a prize. They urge you to respond quickly to collect your prize, and may ask you to click a link

yappusa.com · Spammers often send emails claiming that you have won a sweepstakes or a prize. They urge you to respond quickly to collect your prize, and may ask you to click a link

ANNUAL PROGRESS REPORT2018...Box 10: The MoEC’s Diklat Berjenjang Program Received the UNESCO - Hamdan bin Rashid Al-Maktoum Prize 41 Box 11: Sukabumi Districts - Sustaining the

ANNUAL PROGRESS REPORT2018...Box 10: The MoEC’s Diklat Berjenjang Program Received the UNESCO - Hamdan bin Rashid Al-Maktoum Prize 41 Box 11: Sukabumi Districts - Sustaining the

LDG NEWS · 2018-02-27 · NEWSLETTER - THIRTY / DECEMBER 2015 / EDITORIAL We hope that you all ... 2014 for over 70 years. ... November 1st Prize Nos 51 2nd Prize Nos 147 3rd Prize

LDG NEWS · 2018-02-27 · NEWSLETTER - THIRTY / DECEMBER 2015 / EDITORIAL We hope that you all ... 2014 for over 70 years. ... November 1st Prize Nos 51 2nd Prize Nos 147 3rd Prize

You could be 90 seconds 500...SPONSORED BY: Speak up. Work safe. First prize: $500 Second prize: $400 Third prize: $300 Winners’ schools will receive a matching prize. youngemployeesafety.org

You could be 90 seconds 500...SPONSORED BY: Speak up. Work safe. First prize: $500 Second prize: $400 Third prize: $300 Winners’ schools will receive a matching prize. youngemployeesafety.org

CONDOBOLIN HIGH SCHOOL NEWSLETTER...from a year group box and each winner receives a $20 canteen voucher. When is the prize draw? Prize draws will take place every second Friday. Our

CONDOBOLIN HIGH SCHOOL NEWSLETTER...from a year group box and each winner receives a $20 canteen voucher. When is the prize draw? Prize draws will take place every second Friday. Our

MEDICINE PRIZE 2018 - Nobel Prize Museum · THE NOBEL PRIZE NOBEL PRIZE LESSONS THE NOBEL PRIZE IN PHYSIOLOGY OR MEDICINE 2018. The Nobel Prize in Physiology or Medicine . Since 1901

MEDICINE PRIZE 2018 - Nobel Prize Museum · THE NOBEL PRIZE NOBEL PRIZE LESSONS THE NOBEL PRIZE IN PHYSIOLOGY OR MEDICINE 2018. The Nobel Prize in Physiology or Medicine . Since 1901

Sauk County 4-H NewsletterJan 01, 2020  · a prize from the prize box. Welcome to Sauk County 4-H! ... October 19- Kari Mould, Reedsburg, $20 October 20- Mary Ramsden, Eagle River,

Sauk County 4-H NewsletterJan 01, 2020  · a prize from the prize box. Welcome to Sauk County 4-H! ... October 19- Kari Mould, Reedsburg, $20 October 20- Mary Ramsden, Eagle River,

SCHOOL FAIR PRIZE BOOK - Stratford Ag Society · SCHOOL FAIR PRIZE BOOK Convener: Marlene Ballantyne 271-4873 ... ST4 Collection of 4 different envelope openers in a suitable box.

SCHOOL FAIR PRIZE BOOK - Stratford Ag Society · SCHOOL FAIR PRIZE BOOK Convener: Marlene Ballantyne 271-4873 ... ST4 Collection of 4 different envelope openers in a suitable box.

BUTTERFLIES: SECOND PRIZE — IMMATURES: FIRST PRIZE ...

BUTTERFLIES: SECOND PRIZE — IMMATURES: FIRST PRIZE ...

“Stop Selling Product; Start Selling YOU” THE PO Box 609 ... · » 2016 Spring Show Dates See inside poster right » Grand Prize Information ... presentation that will make an

“Stop Selling Product; Start Selling YOU” THE PO Box 609 ... · » 2016 Spring Show Dates See inside poster right » Grand Prize Information ... presentation that will make an

prize in a treasure hunt. Meaning is something you …...Meaning is not something you stumble across, like the answer to a riddle or the prize in a treasure hunt. Meaning is something

prize in a treasure hunt. Meaning is something you …...Meaning is not something you stumble across, like the answer to a riddle or the prize in a treasure hunt. Meaning is something

TOTAL PRIZE VALUE $68,000 First Prize $22,000

TOTAL PRIZE VALUE $68,000 First Prize $22,000

BUTTERFLIES: SECOND PRIZE — IMMATURES: FIRST PRIZE ... · FIRST PRIZE — BUTTERFLIES: Diaethria clymena (Nymphalidae), Rondonia, ... FIRST PRIZE — IMMATURES: Cerura sp. ... Catopsilia

BUTTERFLIES: SECOND PRIZE — IMMATURES: FIRST PRIZE ... · FIRST PRIZE — BUTTERFLIES: Diaethria clymena (Nymphalidae), Rondonia, ... FIRST PRIZE — IMMATURES: Cerura sp. ... Catopsilia