Reading Quiz 4 Solutions
1. Possible responses:
- Assigning a quantitative estimate to risk may require unreasonable
assumptions.
- Quantitative estimates of risk may be wrong or misleading if the
model or data used to estimate the risk are wrong (e.g., assuming
independence when this is not warranted).
- Some things are very difficult or impossible to quantify
(e.g., human suffering, emotional effects, or social issues)
2. Here is how you could have computed the answer.
Let p denotes the fraction of US cattle that are infected (we
are trying to solve for p). Therefore, if we test one randomly
selected cow, the probability that no infection is detected is
1-p.
Suppose we are testing 10,000 cattle. The probability that none
of the cattle tested are infected is (1-p)^10000, since this is
the probability of 10,000 independent events, each with probability
1-p. Therefore, the probability that at least one of the cattle
tested is infected is 1 - (1-p)^10000.
Suppose we want at least a 99% chance of detecting at least
one infected animal. Then this means we need the following equation
to be true:
1 - (1-p)^10000 >= 99%.
Solving this for p gives the desired answer.
Your particular quiz may have had slightly different numbers
(instead of 10,000 and 99%), but you could use the same procedure
to compute the answer.
3. Thanks for your comments and feedback