BIOS 603

• Learning Objective 4

  
  1. You flip a coin three times. The coin is fair so that the probability of a head is .5. What is the probability that
  

      a.  all three flips are heads?
      b.  the first is a head or the second is a head?
      c.  you get two heads?
      d.  you get two heads given that the first is a head?
      e.  the second is a head given the first is a head?
  

  
  
  2. Work the problem again using an unfair coin. The probability of a head is .6.
  
  Answer

• Learning Objective 5

  The following data was reported by the CDC in The Morbidity and Mortality Weekly Report, 1990, 39(14), 228-232. The Florida Department of Health and Rehabilitative Services interviewed fifty three patients with hepatitis A and sixty four of their disease free eating companions concerning their oyster consumption.

                             Oysters
                            No    Yes  Total
                Cases        2     51    53   
                Controls    31     33    64
                Total       33     84   117
  
  What is the probability that:
  
  a.  A person in this sample was a case?
  b.  A person ate oysters given that s/he was a case?
  c.  A person ate oysters given that s/he was not a case?
  d.  A person ate oysters and was a case?
  
  Are case status and oyster consumption independent?
  

  
  Answer

• Learning Objective 6

  
  
  Relative Risk
  Schiffman, et al (1993) explored the relationship between infection with Human Papillomavirus (HPV) and incidence of cervical epithelial neoplasm (CIN). the following data was adapted from their paper.

                    HPV
           CIN    no     yes
            no  16,849  3.624  20,473
           yes     127    546     673
                16,976  4,170  21,146
  

  a. What is the probability that a person positive for HPV has CIN? b. What is the probability that a person negative for HPV has CIN? c. What is the relative risk for HPV for CIN?
  
  Schiffman, M., Bauer, H., Hoover, R., Glass, A., Cadell, D., Rush, B., Scott, D. Sherman, M., Kurman, R., Wacholder, S., Stanton, C. and Mamos, M. (1993) Epidemiologic evidence showing that human papillomavirus infectin causes most cervical intrapepithelial neoplasia. "Journal of the National Cancer Institute. 85:958-964. Answer

• Learning Objective 7

  
  
  Laws of Probability
  Twenty percent of the students in a certain school smoke cigarettes and 80% do not. The probability that a smoker also drinks is 75%, and the probability that a nonsmoker drinks is 25%. What is the probability that a student drawn at random drinks?
  
  Answer

• Learning Objective 8

  
  
  Laws of Probability
  Use the smoking and drinking problem described above. Build a two by two table based on a sample of 1000 students. a. How many students are in the no smoking and no drinking cell? b. What is the probability that a student smokes given that he or she drinks?
  Answer

• Learning Objective 9

  
  
  Sensitivity and Specificity
  
  
  The prevalence of chlamydia is 1%. The sensitivity of a screening test is 92% and the specificity equals 99%. A woman is told that she has a positive test result. What is the probability that she has chlamydia?
  Answer

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