Greenwood press

PROBABILITY
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ties in the state, but as recently as 1998, two candidates who were tied in the elec-
tion for mayor of Estancia, New Mexico, opted to play five-card stud for the job. 
Statisticians use probabilities and relative frequencies in determining relation-
ships. A key concept from probability is the idea of independence. The formal
mathematical definition of independence is given in the equation 
P (A + B) =
P (A) • P (B). If two events, A and B, are independent, then the probability of
them both happening is the product of the separate probabilities. The concept of
independence is behind investigations such as the Physicians’ Health Study,
which tested the effects of aspirin on over 22,000 doctors. Half the doctors were
given a daily dose of aspirin, and half were given a neutral pill (placebo). Doctors
didn’t know what kind of pill they received. The researchers periodically con-
tacted the participants to find out if the physician had suffered a heart attack. The
results showed that 0.9 percent of the participants who received aspirin had heart
attacks, and 1.7 percent of those with the placebo had heart attacks. Although it
looks like the percents favor aspirin, the percents are so small that it is possible
they were due to chance. The study data is shown on the following table. This is
called a contingency table.