Question

1. The CDC is using a rapid diagnostic test to measure the incidence of cholera in the Florida. It was determined that the probability of a + test given cholera was 95% while the probability of a - test given no cholera was 80%. It is estimated that 6% of the Floridian population may have cholera. a. Draw and label a tree diagram. Use N=10,000 for the population. Please draw and label completely this diagram with the Disease Status in primary branches and the + and –in secondary branches. The labels will include Disease, No Disease, False -, False +, True -, True +, numbers, probability formulas and the decimal equivalent. What do the + and the – branches mean in words? b. Calculate and label a 2X2 table. c. If a Floridian receives a + test, what is the probability that he has cholera. Use Bayes’ Rule. Write the formula, all calculations, the answer. Verify with the 2X2 table. d. What is the probability that a Floridian has a + test?

2. The state of Connecticut reports that 25% of all Dengue Fever patients are female. What is the probability that the next 2 patients diagnosed with Dengue Fever will be males?

3. Governor Cuomo is questioning vendors regarding the sale of test kits to diagnose meningitis in New York. He asks them 7 questions in which 4 questions are identical and 2questions are identical. How many different ways can he inquire?

4. How many different arrangements can be made from “GENEVIEVE”?

5. Gregor Mendel, the father of genetics, demonstrated that the colored petal of the experimental flower was purple. The gene for this purple color was the protein, Pp. He isolated this protein. a. Mendel flips the genes 4 times, what is the probability he obtains exactly 2 of the same outcomes on each flip? Show A tree. b. Mendel flips the genes 4 times, what is the probability he obtains exactly at least 1P? Show a tree. c. The probability that Mendel will obtain a purple gene in any given laboratory flower experiment is 0.20. What is the probability that he will obtain the purple genes in 3 lab experiments in a row?

6. A gene for Yellow Fever has 6 chromosomes: 1,2,3,4,5,6 on its mutating side. Given a mutation, what is the probability that exactly an even numbered chromosomes will appear?

7. In the lottery, a person selects 5 different numbers from 1 to 56 (inclusive) and then another (a sixth number called the Mega Ball) from 1 to 46 (inclusive). If the first 5 numbers match the player’s numbers in any order along with the Mega Ball number, the player wins. a. What is the total number of winning arrangements? b. What is the probability of winning?

8. A total of 200 men and women were surveyed by the CDC to determine their exposure to 3 diseases: Sleeping Sickness (SS), Typhoid Fever (TF), and Tb (Tb). Of the sample, 60% were men. Of the men 10% had SS, 40% had Tb, and the remainder had TF. Of the women, 50% had TF, 20% had Tb, and the remainder had SS. Pick one person at random what is the: 1. P(X=SS) 2. P(X=Tb or TF) 3. P(X=SS and TF) 4. P(X=Man/Tb) 5. P(X=SS/Woman) 6. P(X=TF or Woman) 7. P(X=SS and Woman) 8. P(X=Tb or Man) 9. P(X=Woman or SS) 10. I will pick randomly one person from the sample. Tell that person to go home. Pick another. Tell that person to go home. Pick another. What is the probability that all 3 people had SS?

Answer 1