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Example 3: The idea of red-light cameras has been disputed quite often in Arizona and all across
the United States. While unable to find any specific details, the author will assume that red-light
runners have about a 70% chance of being caught by a red-light camera on any given instance.
Suppose that on a given day, two cars run through an intersection during separate red lights,
setting off the camera. What is the probability that both drivers are
caught
SOLUTION: We can fairly assume that the first driver being caught
and the second driver being caught (calling these events and ,
respectively) constitute events that do not affect one another. Thus,
( ) ( ) ( )
There is a 49% chance that both drivers are caught. This is about the likelihood of getting heads
on the toss of a coin.
Example 5: In a crop of corn, the Food & Drug Administration
(FDA) finds that two of the 20 bushels of corn are potentially
contaminated with E. coli. Supposing that two bushels have
already gone out for shipment to county marketplaces, how likely
is it that both of the contaminated bushels have gone out
SOLUTION: The question asks about the probability that both
have been shipped, that is, the first contaminated bushel and the
second contaminated bushel. We will refer to these events as simply and . We will first
write the “and” probability in the form of dependent events and will then determine whether or
not a dependency exists (see Independence Property box above).
( ) ( ) ( )
We know that ( ) . Now, since the first probability “removes” one of the two
contaminated bushels and one bushel out of the 20 available, the probability of shipping a second
bushel is slightly changed to:
( )
Thus, the events are indeed dependent, and so the probability becomes:
( )
Statistics for Decision-Making in Business © Milos Podmanik Page 92