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This means that if samples of HFCS were to be sampled randomly and repeatedly, it would be
found that 45% of all samples would contain traces of mercury. This does not guarantee that
exactly 45 samples out of 100 will contain mercury.
Example 3: In July 2011, temperatures in Gilbert, Arizona were above 100 every day
(SOURCE: www.weather.com). Based on this data, a researcher concludes that the probability of
above 100 temperatures in Arizona is 100%. Comment on his findings.
SOLUTION: Since temperatures in July 2011 were above 100 31 days of the 31 days in the
month, it is fair to make the experimental observation that approximately 100% of all days in
July 2011 have temperatures exceeding 100 , in the long-run (there have been days in the past
when temperatures were below 100 ); However, because we know that temperatures are
periodic, or that they go from low to high and back to low over the course of a year, 100% is not
a good estimate for temperatures in Arizona, in general (temperatures are reasonably never above
100 in January!).
This example truly stresses the importance of critical thinking when using probabilities. It is
often that probabilities are used and abused in the media, education, and in politics, just to name
a few. We want to make sure that we are as specific as possible.
It will often be considerably helpful to display probabilities in a tabular form, that is, through the
use of tables. This type of table is called a contingency table. This not only helps to organize
data, but to simultaneously see the big picture. Let‟s consider an example.
Example 4: In a 1950 study that considered 1,418 hospital patients in London (half of each) with
and without lung cancer and whether or not they smoked over the course of their lives, the
following was found:
Smoker/Lung Cancer Yes No
Yes 688 650
No 21 59
Assuming this data can be used as a representation of the entire population of London residents,
analyze the data by discussing the following:
a. What is the probability that a randomly selected participant within this study develops
lung cancer
b. Provided that a person was a smoker, what is the probability that he has lung cancer
c. Provided that a person was not a smoker, what is the probability that he has lung cancer
d. Given that a person has lung cancer, what is the probability that he smokes
SOLUTION:
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