NAME:
MAE 108 – Probability and Statistical Methods for Engineers  Winter 2010
Midterm # 1
 January 29, 2010
50 minutes, open book, open notes, calculator allowed, no cell phones.
Write your answers directly on the exam. 50 points total.
(1) (10 points)
A total of 28 percent of all roads in the US suffer from severe traffic jams, 7 percent are subject
to very cold weather, and 5 percent are subject to both traffic jams and very cold weather. What
percentage of rods in the US have neither traffic jams nor very cold weather?
Solution:
E
=
{
the road has traffic jams
}
F
=
{
the road has cold weather
}
A
=
{
the road has neither traffic jams nor very cold weather
}
.
We have
A
=
¯
E
¯
F
so
P
(
A
) =
P
(
¯
E
¯
F
) = 1

P
(
E
∪
F
) = 1

P
(
E
)

P
(
F
) +
P
(
EF
) = 1

0
.
28

0
.
07 + 0
.
05 = 0
.
70.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
(2) (10 points)
An insurance company believes that people who purchased insurance can be divided into two classes:
those who are accident prone, and those who are not. Their statistics show that an accidentprone
person will have an accident within a fixed 1year period with a probability of 40%, whereas this
probability decreases to 20% for a nonaccidentprone person. If we assume that 30 percent of the
population is accident prone, what is the probability that a person will have an accident within a
year of purchasing a policy?
This is the end of the preview.
Sign up
to
access the rest of the document.
 Winter '10
 Lauga
 Conditional Probability, Probability, Probability theory, Cumulative distribution function

Click to edit the document details