PrepTest 106, Section 2, Question 7
For every 50 dogs that contract a certain(50 more words not shown)
Which one of the following(13 more words not shown)
- Athe total number(11 more words not shown)
- Bwhether the vaccine(11 more words not shown)
- Cthe number of(13 more words not shown)
- Dthe likelihood that(9 more words not shown)
- Ethe likelihood that(9 more words not shown)
Reading the argument
How likely is the dog to catch the disease in the first place? One death per 50 infected dogs isn't one death per 50 dogs overall.
The vaccine's risk applies to dogs receiving the vaccine. The disease's one-in-50 risk applies only after a dog contracts the disease. Comparing those numbers directly skips the chance of infection.
Suppose only one in 1,000 unvaccinated dogs catches it. Among 50,000 such dogs, that would mean 50 infections and about one death from the disease. Vaccinating 50,000 dogs, by contrast, would bring about ten deaths from vaccine complications at the stated rate of one per 5,000. That example would make the argument's conclusion much less convincing.
Now suppose one in ten unvaccinated dogs catches the disease. Among the same 50,000 dogs, there would be 5,000 infections and about 100 disease deaths. Preventing virtually all those infections at a cost of about ten vaccination deaths would support the safety comparison. These are hypothetical numbers showing why the missing infection rate matters.
What we’re looking for
The question asks which information would help evaluate the argument. We want the fact that lets us decide which kind of situation we're in: how likely an unvaccinated dog is to contract this disease.
Working the answers
- A
A total of deaths from all causes doesn't separate the risks affected by this vaccine from unrelated risks. Dogs could die from many other causes without changing whether vaccination reduces deaths associated with this disease. We need the missing infection probability, not a count that combines everything.
- B
Whether the vaccine works in other household pets doesn't settle the comparison for dogs. It could work wonderfully in cats or fail completely in cats while the unanswered question about dogs' risk of catching the disease remained exactly the same.
- C
Deaths from other diseases don't tell us how often unvaccinated dogs contract this disease. No connection is given between the vaccine and those other deaths. Counting them would not fill the gap between the fatality rate among infected dogs and the risk facing an unvaccinated dog.
- D
This asks for a probability, but it is the probability of the wrong disease. The argument concerns a vaccine against one particular disease. Without a stated connection to another disease such as rabies, that other infection risk doesn't help determine the benefit of this vaccine.
- ECorrect
A high infection risk makes preventing this disease more valuable; a very low infection risk means many vaccinated dogs would take the vaccine's risk even though they were unlikely to face the disease's risk.
This information lets us combine the chance of contracting the disease with the one-in-50 chance of dying after contracting it. Only then can we meaningfully compare that risk with the vaccination risk. We don't need to assume every unvaccinated dog gets sick, but we do need to know how often it happens.
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