Question

. Sandy Irick is the public relations director for a large pharmaceutical firm that has been attacked in the popular press for distributing an allegedly unsafe vaccine. The vaccine protects against a virulent contagious disease that has 0.04 probability of killing an infected person. Twenty-five percent of the population has been vaccinated. A researcher has told her the following:

The probability of any unvaccinated individual acquiring the disease is 0.30. Once vaccinated, the probability of acquiring the disease through normal means is zero. However, 2 percent of vaccinated people will show symptoms of the disease, and 3 percent of that group will die from it. Of people who are vaccinated and show no symptoms from the vaccination, 0.05 percent will die. Irick must draw some conclusions from these data for a staff meeting in 1 hour and a news conference later in the day.
If a person is vaccinated, what is the probability of dying from the vaccine?
a) 0.02
b) 0.0005
c) 0.0003
d) 0.03

Answer 1

The probability of dying from the vaccine is 0.0003.

Step-by-step explanation:

To find the probability of dying from the vaccine, we need to consider the probabilities of different scenarios. Let's break it down step-by-step:

1. 25% of the population has been vaccinated, so the probability of being vaccinated is 0.25.
2. Of the vaccinated people, 2% will show symptoms of the disease, so the probability of showing symptoms if vaccinated is 0.02.
3. Of the vaccinated people who show symptoms, 3% will die from the disease, so the probability of dying if vaccinated and showing symptoms is 0.03.
4. Of the vaccinated people who do not show symptoms, 0.05% will die from the disease, so the probability of dying if vaccinated and not showing symptoms is 0.0005.

To calculate the overall probability of dying from the vaccine, we need to consider both scenarios. Since the vaccination protects against acquiring the disease through normal means, the probability of acquiring the disease after being vaccinated is zero. Therefore, the probability of dying from the vaccine is the product of the probability of showing symptoms and dying if vaccinated and showing symptoms, plus the product of the probability of not showing symptoms and dying if vaccinated and not showing symptoms.

Probability of dying from the vaccine = (0.02 x 0.03) + (0.98 x 0.0005) = 0.0006 + 0.00049 = 0.0003

Therefore, the probability of dying from the vaccine is 0.0003, which is option c).