Task: Consider a family with a mother, father and two children. Let A1 = (mother has influenza}, A2 = (father has influenza}, A3 = (first child has influenza}, A4 = (second child has influenza), B = (at least one child has influenza), C = (at least one parent has influenza}, and D = (at least one person in the family has influenza).
1 What does A1 υ A2 mean?
2 What does A1 n A2 mean?
3 Are A3 and A, mutually exclusive?
4 What does A3 υ B mean?
5 What does A3 n B mean?
6 Express C in terms of A1, A2, A3, and A4.
7 Express D in terms of B and C.
8 What does A1‾ mean?
9 What does A2‾ mean?
10 Represent C‾ in terms of A1, A2, A3, and A4.
11 Represent D‾ in terms of B and C.
Suppose an influenza epidemic strikes a city. In 10% of families the mother has influenza; in 10% of families the father has influenza; and in 2% of families both the mother and father have influenza.
12 Are the events A1 = (mother has influenza} and A2 = (father has influenza) independent?
Suppose there is a 20% chance each child will get influenza, whereas in 10% of two-child families both children get the disease.
13 What is the probability that at least one child will get influenza?
14 Based on Problem 12, what is the conditional probability that the father has influenza given that the mother has influenza?
Q1. Using Question 12 in your textbook, are the events independent? Explain your answer.
Q2. Using Question 13 in your textbook, what is the probability that at least one child will get influenza?
Q3. Using Question in your textbook, based on problem 12, what is the conditional probability that the father has influenza given that the mother has influenza?
Q4. Using Question 17 from your textbook, what is the probability that at least one of the women has Alzheimer's disease?
Q5. Using Question 93 in your textbook, if the clinical diagnosis is considered a screening test for Alzheimer's disease, then what is the sensitivity of this test? Use 3 decimal places in your calculation.
Q6. Using Question 14 in your textbook, if 500 newborns are screened at the inner-city hospital, then what is the exact binomial probability of 5 HIV-positive test results? Use 4 decimal places in your calculation.
Q7. Using Question 25 in your textbook, suppose 10 gonorrhea cases are reported over a 3-month period among 10,000 people living in an urban county. The statewide incidence of gonorrhea is 50 per 100,000 over a 3-month period. Is the number of gonorrhea cases in this county unusual for this time period? Use 3 decimal places in your calculation and explain your answer.
Q8. Using Question 31 in your textbook, if the normal range is 65-120 mg/dL, then what percentage of values will fall in the normal range? Use 2 decimals in your calculation, then convert it to a percentage to hep explain your answer.
Q9. Using Question 35 in your textbook, suppose that in a pharmacologic study involving 6,000 patients, 75 patients have blood-glucose levels at least 1.5 times the upper limit of normal on one occasion. What is the probability that this result could be due to chance? Use 4 decimal places in your calculation and explain your answer.