186 Fundamentals of Statistics
To fi nd the probability of a set of discrete events, we simply add up the
individual probabilities of each event in the set. So to fi nd the probability of
two or fewer accidents occurring at the intersection we add up the probabil-
ities of no accidents (.050), 1 accident (.149), and 2 accidents (.224) to arrive
at an overall probability of .423, or about 42%. Because the total probability
is 1, the probability of more than two accidents occurring at the intersection
would thus be 58%.Continuous Probability Distributions
In continuous probability distributions, probabilities are assigned to a range
of continuous values rather than to distinct individual values. For example,
consider a person shooting at a target. The distribution of shots around the
bull’s eye follows a continuous distribution. If the shooter is good, the prob-
ability that the shots will cluster closely around the bull’s eye is very high
and it is unlikely that a shot will miss the target entirely.
Continuous probability distributions are calculated using a probability
density function (PDF). When we plot a PDF against the range of possible
values, we get a curve in which the curve’s height indicates the position of
the most likely values. Figure 5-3 shows a sample PDF curve.Figure 5-2
Poisson
probability
distribution
for car
accident
data