Suppose that a corpse is brought to a morgue and the coroner is asked to assess the probability that

Suppose that a corpse is brought to a morgue and the coroner
is asked to assess the probability that the cause of death was pancreatic
cancer (as contrasted to some other cause of death). Before examining the
corpse, the best estimate that the coroner can make is 1.4%, the death rate
from pancreatic cancer in the general population. Now suppose the coroner
performs a test for pancreatic cancer that is 99% accurate, both in the sense
that if the cause of death was pancreatic cancer, the probability is 99% that
the test results are positive, and if the cause of death was something else,
the
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Suppose that a corpse is brought to a morgue and the coroner
is asked to assess the probability that the cause of death was pancreatic
cancer (as contrasted to some other cause of death). Before examining the
corpse, the best estimate that the coroner can make is 1.4%, the death rate
from pancreatic cancer in the general population. Now suppose the coroner
performs a test for pancreatic cancer that is 99% accurate, both in the sense
that if the cause of death was pancreatic cancer, the probability is 99% that
the test results are positive, and if the cause of death was something else,
the probability is 99% that the test results are negative. Let the cause of
death be represented by the variable, D, which can take two discrete values, C,
for pancreatic cancer and E, for something else. The test is represented by the
variable, T, which can take two values, Y for positive and N for negative. (A)
Write down the 2  2 table of the conditional
probabilities P(D|T). (B) Suppose the test results are negative. Use Bayesian
Inference to assess the probability that the cause of death was pancreatic
cancer. (C) How can the statement that the test is 99% accurate be used in a
misleading way?

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