2 6 0C HaP Te r 1 1 ■ C h a n c e s- What would Wendy’s chances of having colon cancer be if the other
probabilities remained the same as in the original example, except that
the conditional probability that the test is positive, given that the patient
does not have colon cancer, is 1 percent (or 0.01)? - What would Wendy’s chances of having colon cancer be if the other
probabilities remained the same as in the original example, except that
the conditional probability that the test is positive, given that the patient
does not have colon cancer, is 10 percent (0.1)? - Chris tested positive for cocaine once in a random screening test. This
test has a sensitivity and specificity of 95 percent, and 20 percent of the
students in Chris’s school use cocaine. What is the probability that Chris
really did use cocaine? - As in problem 7, 20 percent of the students in Chris’s school use cocaine,
but this time Chris tests positive for cocaine on two independent tests,
both of which have a sensitivity and specificity of 95 percent. Now what
is the probability that Chris really did use cocaine? - In your neighborhood, 20 percent of the houses have high levels of
radon gas in their basements, so you ask an expert to test your basement.
An inexpensive test comes out positive in 80 percent of the basements
that actually have high levels of radon, but it also comes out positive
in 10 percent of the basements that do not have high levels of radon. If
this inexpensive test comes out positive in your basement, what is the
probability that there is a high level of radon gas in your basement? - A more expensive test for radon is also more accurate. It comes out
positive in 99 percent of the basements that actually have high levels
of radon. It also tests positive in 2 percent of the basements that do not
high levels of radon. As in problem 7, 20 percent of the houses in your
neighborhood have radon in their basement. If the expensive test comes
out positive in your basement, what is the probability that there is a high
level of radon gas in your basement? - Late last night a car ran into your neighbor and drove away. In your
town, there are 500 cars, and 2 percent of them are Porsches. The only
eyewitness to the hit-and-run says the car that hit your neighbor was
a Porsche. Tested under similar conditions, the eyewitness mistakenly
classifies cars of other makes as Porsches 10 percent of the time, and
correctly classifies Porsches as such 80 percent of the time. What are the
chances that the car that hit your neighbor really was a Porsche? - Late last night a dog bit your neighbor. In your town, there are 400 dogs,
95 percent of them are black Labrador retrievers, and the rest are pit bulls.
The only eyewitness to the event, a veteran dog breeder, says that the
dog who bit your neighbor was a pit bull. Tested under similar low-light
conditions, the eyewitness mistakenly classifies black Labs as pit bulls
only 2 percent of the time, and correctly classifies pit bulls as pit bulls
90 percent of the time. What are the chances that dog who bit your
neighbor really was a pit bull?
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