Chrome File Edit View History Bookmarks Profiles Tab Window Help P Q 8 Sat Feb 25 9:14 AM Movies7 | Watch Family C X B Discussions List - FIN 20 x Math 120 Introduction to x New chat X NAS Part 1 - Class A, E, a X Paraphrasing Tool - Quill X -7 C courses.maine.edu/d21/le/dropbox/263442/393975/DownloadAttachment?fid=19320066 Update Movies7.to | Watc... Google Docs @ Homepage - Univ... Watch Anime Onli... Select a Course -... Dashboard Playground - Ope... @ MA120 =Math 120 Introduction to Statistics 1 / 3 75% + MAT 120 Introduction to Statistics Activity #5: Probability PART 1 - In this activity we are going to first work with conditional probability, is defined on page 281. Answer questions 1 - 8 and compare your solutions with that of a classmate. Definition: Condit : Conditional Probability 1 The conditional probability of F given E, read P(FIE), is the probability that F occurs, given that E is known to have occurred. P(F E) = P(E and F) _ N(E and F) P(E N(E ACTIVITIES: When women turn 40, their physicians typically remind them that it is time to undergo mammography screening for breast cancer. The data in the following table are based on 100,000 U.S. women, ages 40 to 50, who participated in mammography screening. Assume the sample is representative of this population, and note that medical tests can be positive or negative, regardless of whether or not a patient has the condition. 2 Has Breast No Breast Cancer Cancer subtotals Positive Mammogram 720 6,944 7,664 Negative Mammogram 80 92,256 92,336 subtotals 800 9,200 | Grand Total: 100,000 Answer questions 1 - 8 and compare your answers with a classmate. For a woman, age 40-50, selected at random, find the probability that she: 1. has breast cancer? does not have breast cancer? 2. has a positive mammogram? has a negative mammogram? 3 3. has a positive mammogram, given that she has breast cancer? This is known as the sensitivity of the test. 4. has a negative mammogram, given that she does not have breast cancer? This is known as the specificity of the test.6 Chrome File Edit View History Bookmarks Profiles Tab Window Help 4 (D >E . V Movies7|Watch Familx X 3 Discussions List-FIN. x 6 Math120 Introductiont X l@ New chat X e NAS Part'l-Class A,E x N C' , courses.maine.edu Q d] i} v Movies7.to | Watc... Google Docs I3 Homepage - Univ... Watch Anime Onli... 7/) Select a Course -... G, Dashboard Playground Ope... B MA'IZO _ Math120 Introduction to Statistics 2 / 3 75% + E] 0:) 5. has breast cancer given that she has a positive mammogram? This is the positive-predictive value of the test. 6. does not have breast cancer. given that she has a negative mammogram? This is called the negative-predictive value of the test. 7. has a positive mammogram, given that she does not have breast cancer? This is known as the false-poslllve rate. 8. has a negative mammogram. given that she has breast cancer? This is known as the false-negative rate. PART 2 Problem Solving Using Probability Rules Solve the following and check your answers with a classmate. 1. At a fast-food restaurant, 60% of the patrons order a burger. Of those ordering a burger' 40% also order fries. If a patron is randomly selected, what is the probability that they ordered a burger and fries? . About 13% of the population is left handed. Assume that three persons are independently selected. What is the probability that a. All three are not left-handed? b. At least one is left-handed? . According to the Children's Oncology Group Research Data Center at the University of Florida, 20% of children with neuroblastoma undergo surgery rather than the traditional treatment of chemotherapy or radiation. The surgery is successful in curing the disease 95% of the time. Consider a child diagnosed with neuroblastoma. What are the chances that the child undergoes surgery and is cured? (Source: Explore, Spring 2001) 6 Chrome File Edit View History Bookmarks Profiles Tab Window Help (9 >l O Movies7 | Watch Familn~ X 3 Discussions List - FIN. x 6 Math 120 Introduction t X l@ New chat X e NAS Part 'l - Class A, E x N C' , courses.maine.edu . Movies7.to | Watc... Q [D '1} G Google Docs I3 Homepage - Univ... Watch Anime Onli... 7/) Select a Course -... G, Dashboard Playground Ope... B MA'IZO _ Math120 Introduction to Statistics 3 / 3 75% + E] 0:) 4. A group of students who listened to podcasts was asked about the apps they use for this purpose. 55% said they used Spotify, 24% said they use Audible and 15% use both oi these apps. 36% of the students reported using neither of these apps. Imagine a student from this group is selected at random. a. What is the probability that a student uses Spotify or Audible? b. Are the events \"student uses Spotify" and \"student uses Audible" mutually exclusive? Explain. c. What is the probability that a student uses Spotify. given that they use Audible? d. Are the events \"student uses Spotify" and \"student uses Audible" independent? Explain. 5. The probability that a train leaves on time is 0.9 and the probability that it both leaves on time and arrives on time is 0.75. If the train leaves on time, what is the probability that it arrives on time