Letdenote the probability of getting a disease if vaccinated, anddenotes the probability of getting the disease if unvaccinated, then vaccine efficacy (VE) is                                      . That is, VE is a relative probability concept becauseis divided by. Suppose there are 1,000 people in the vaccinated (i.e., treatment) group, and 1,400 in the unvaccinated (i.e., control or placebo) group. Also, suppose that 5 people in the vaccinated group contract the disease and 85 people in the unvaccinated group contract the disease. Calculate the vaccine efficacy VE.

The sensitivity (true positive rate) and specificity (true negative rate) of a laboratory test for a certain virus are 70% and 99%, respectively. If 0.5% of the population currently has the virus, what is the probability that a person has the virus given that the test result is positive?

Regifting is defined as the act of taking a gift that has been given to you and presenting it as a gift to someone else. According to survey conducted by a credit card company regarding consumer spending, 81% of the respondents felt that it was socially acceptable to regift during the holiday season (big sigh of relief). Suppose a random sample of 10 holiday shoppers was selected. Complete parts a through d. a. What is the probability that 9 shoppers from this sample felt that regifting was socially acceptable? The probability is. (Type an integer or decimal rounded to four decimal places as needed.) b. What is the probability that more than 7 shoppers from this sample felt that regifting was socially acceptable? The probability is. (Type an integer or decimal rounded to four decimal places as needed.) c. What is the probability that fewer than 10 shoppers from this sample felt that regifting was socially acceptable? The probability is (Type an integer or decimal rounded to four…

A blood bank asserts that a person with type O blood and a negative Rh factor (Rh−) can donate blood to any person with any blood type. Their data show that 49% of people have type O blood and 17% of people have Rh− factor; 52% of people have type O or Rh− factor. A. Find the probability that a person has both type O blood and the Rh− factor. B. Find the probability that a person does NOT have both type O blood and the Rh− factor.