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Critical Thinking: Interpreting results from a test for smoking

It is estimated that roughly half of smokers lie when asked about their smoking involvement. Pulse Co-Oximeters may be a way to get information about smoking without relying on patients鈥� statements. Pulse CO-oximeters use light that shines through a fingernail, and it measures carbon monoxide in blood. These devices are used by firemen and emergency departments to detect carbon monoxide poisoning, but they can also be used to identify smokers. The accompanying table lists results from people aged 18鈥�44 when the pulse CO-oximeters is set to detect a 6% or higher level of carboxyhemoglobin (based on data from 鈥淐arbon Monoxide Test Can Be Used to Identify Smoker,鈥� by Patrice Wendling, Internal Medicine News, Vol. 40., No. 1, and Centers for Disease Control and Prevention).

CO-Oximetry Test for Smoking

Confusion of the Inverse Find the following values, then compare them. In this case, what is confusion of the inverse?

$P\left(Smoker|Positive鈥�鈥�test鈥�鈥�result\right)$

$P\left(Positive鈥�鈥�test鈥�鈥�result|鈥�鈥�smoker\right)$

In Exercises 5鈥�36, express all probabilities as fractions.

Grading Exams Your professor has just collected eight different statistics exams. If these exams are graded in random order, what is the probability that they are graded in alphabetical order of the students who took the exam?

In Exercises 9鈥�12, assume that 50 births are randomly selected. Use subjective judgment to describe the given number of girls as (a) significantly low, (b) significantly high, or (c) neither significantly low nor significantly high.

47 girls.