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1.010 Uncertainty in Engineering
Fall 2008
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1.010 Fall 2008
Homework Set #3
Due October 2, 2008 (in class)
1.
The service stations along a highway are located according to a Poisson process with
an average of 1 service station in 10 miles. Because of a gas shortage, there is a
probability of 0.3 that a service station would have no gasoline available. Assume that the
availabilities of gasoline at different service stations are statistically independent.
(a)
What is the probability that there is
at most
1 service station in the next 15 miles
of highway?
(b)
What is the probability that none of the next 3 stations has gasoline for sale?
(c)
A driver on this highway notices that the fuel gauge in his car reads empty; from
experience he knows that he can go another 15 miles. What is the probability that
he will be stranded on the highway without gasoline?
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 Spring '05
 GeorgeKocur
 Probability theory, Poisson process, 4 years

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