PubHlth 540 Fall 2013 Exam II Choice A (Probability) Page 1 of 8

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1 PubHlth 540 Fall 2013 Exam II Choice A (Probability) Page 1 of 8 PubHlth Introductory Biostatistics Fall 2013 Examination II Choice A Unit 2 (Introduction to Probability) Due Monday October 7, 2013 Last submission date for credit: Tuesday October 15, 2013 Clarification of Examination II. You are required to submit an examination II. This can be done in either of 3 ways: (1) You submit Examination II Choice A (this test); or (2) You submit Examination II Choice B (next test); or (3) You submit BOTH Examination II Choices A and B Note - If you choose to attempt both choices A and B, I will take the higher grade. Instructions and Checklist: 1. Start each problem on a new page. 2. Write your name on every page. 3. Make a photo-copy of your exam for safekeeping prior to submission 4. Complete the signature page How to submit your exam: Worcester In-Class Section 1. Bring your completed exam to class on Monday October 7, 2013, being sure that you have made a copy for safe keeping; OR 2. Mail your completed exam to me with post mark October 7, 2013 to my address below. ONLINE Section 1. Upload your completed exam to the ASSIGNMENT tab no later than 11:59 pm on Monday October 7, This must be a single pdf and be named using the convention lastname_exam2a.pdf. 2. Mail your completed exam to me with post mark October 7, 2013 to my address below. Carol Bigelow School of Public Health/402 Arnold House University of Massachusetts/Amherst 715 North Pleasant Street Amherst, MA Tel

2 PubHlth 540 Fall 2013 Exam II Choice A (Probability) Page 2 of 8 PubHlth Introductory Biostatistics Fall 2013 Examination II Choice A Unit 2 (Introduction to Probability) DUE: 11:59 PM Monday October 7, 2013 Last submission date for credit: 11:59 PM Tuesday October 15, 2013 Signature This is to confirm that in completing this exam, I worked independently and did not consult with anyone. Signature: Printed Name: Date:

3 PubHlth 540 Fall 2013 Exam II Choice A (Probability) Page 3 of 8 1. (10 points total) A couple wants to have three children. Assume that the probabilities of a newborn being male or being female are the same and that the gender of one child does not influence the gender of another child. 1a. (5 points) What is the sample space for having three children (gender of the first child, gender of the second child, gender of the third child)? 1b. (5 points). What is the probability of each elementary outcome (gender of the first child, gender of the second child, gender of the third child)

4 PubHlth 540 Fall 2013 Exam II Choice A (Probability) Page 4 of 8 2. (10 points total) The setting is the same as for question #1: A couple wants to have three children. Assume that the probabilities of a newborn being male or being female are the same and that the gender of one child does not influence the gender of another child. This same couple is now wondering how many boys they might get if they have three children. What is the probability model for the number of boys they will get if they have three children. Hint - In specifying your answer, you need to provide two things: the sample space and the probabilities of each outcome in the sample space.

5 PubHlth 540 Fall 2013 Exam II Choice A (Probability) Page 5 of 8 3. (20 points total) A certain research company analyzed the nutritional content of 77 brands of packaged breakfast cereals. For each cereal, one of the measurements made was the fat content (in grams) per serving. Call this random variable X. The following is the probability model for X = fat content (in grams) per serving. 10/2/2013 Correction: X Probability Consider the following two events: A = { fat content is 4 grams or greater } B = { fat content is 5 grams or less } 3a. (5 points) What outcomes make up the event A? What is Probability [ A ]? 3b. (5 points) What outcomes make up the event B? What is Probability [ B]? 3c. (5 points) What outcomes make up the event A or B?. What is Probability [ A or B ]? 3d. (5 points) Why is Probability [A or B] Probability[A] + Probability[B]?

6 PubHlth 540 Fall 2013 Exam II Choice A (Probability) Page 6 of 8 4. (10 points total) The following is the probability model for the blood type of a randomly chosen person in the United States. Blood Type Probability O 0.45 A 0.40 B 0.11 AB??? 4a. (5 points) What is the probability that a randomly chosen person has blood type AB? 4b. (5 points) Suppose Maria has blood type B. She can safely receive blood transfusions from people with blood types O or B. What is the probability that a randomly selected person in the United States can donate blood to Maria?

7 PubHlth 540 Fall 2013 Exam II Choice A (Probability) Page 7 of 8 5. (20 points total) Sickle-cell anemia is a hereditary medical condition affecting red blood cells that is thought to protect against malaria, a debilitating parasitic infection of the liver and blood. That would explain why the sickle-cell trait is found in people who originally came from Africa, where malaria is widespread. A study in Africa tested 543 children for the sickle-cell trait and also for malaria infection. In all, 25% of the children had sickle-cell, and 6.6% of the children had both sickle-cell and malaria. Overall, 34.6% of the children had malaria. Use this information to answer the following. 5a. (5 points) What is the probability that a given child has neither malaria nor sickle-cell? 5b. (5 points) What is the probability that a given child has either malaria or sickle-cell? 5c. (5 points) Perform the necessary calculations and then answer the following question: Are the events sickle-cell trait and malaria independent? 5d. (5 points) What does your answer to #5c suggest to you about the relationship between sickle-cell and malaria? Explain your answer in 1-2 sentences.

8 PubHlth 540 Fall 2013 Exam II Choice A (Probability) Page 8 of 8 6. (30 points total) Enzyme immunoassay tests are used to screen blood specimens for the presence of antibodies to HIV, the virus that causes AIDS. The presence of antibodies indicates the presence of the HIV virus. The test is quite accurate but is not always correct. The following table gives the probabilities of positive and negative test results when the blood tested does and does not actually contain antibodies to HIV. Test Result Positive (+) Negative (-) Antibodies present Antibodies absent Suppose that 1% of a large population carries antibodies to HIV in their blood. 6a. (10 points) Draw a tree diagram for selecting a person from this population (outcomes: antibodies present or absent) and for testing his or her blood (outcomes: test positive or negative). 6b. (10 points) What is the probability that the test is positive for a randomly chosen person for this population? 6c. (10 points) What is the probability that a person in this population has the HIV virus given that he or she tests negative?