STAT 230: Introduction to Probability and
Random Variables
Summer 2009
Solutions for Midterm 1
Exercise
1 (
20pts.
)
A large group of people is to be checked for two common symptoms of a cer
tain disease. It is known that 20% of the people possess symptom A alone, 30%
possess symptom B alone, 10% possess both symptoms, and the remainder pos
sess no symptoms. A person is chosen at random from the group.
(a)Find the probability that the person has neither symptom. (
5pts.
)
P
(
A
0
∩
B
0
) = 1

P
(
A
0
∩
B
) +
P
(
A
∩
B
0
) +
P
(
A
∩
B
) = 1

0
.
3 + 0
.
2 + 0
.
1 =
0
.
4
(b)Find the probability that the person has at least one symptom. (
5pts.
)
P
(
A
∪
B
) = 1

P
(
A
0
∩
B
0
) = 1

0
.
4 = 0
.
6
(c)Find the probability that the person has exactly one symptom. (
5pts.
)
P
(
A
∩
B
0
) +
P
(
A
0
∩
B
) = 0
.
2 + 0
.
3 = 0
.
5
(d)Find the conditional probability that the person has symptom A given
that he has symptom B. (
5pts.
)
P
(
A

B
) =
P
(
A
∩
B
)
P
(
B
)
=
P
(
A
∩
B
)
P
(
B
∩
A
)+
P
(
B
∩
A
0
)
=
0
.
1
0
.
1+0
.
3
= 0
.
25
Exercise
2 (
20pts.
)
A box contains 100 computer chips, of which exactly 5 are good and the re
maining 95 are bad. The following three questions are independent of each other.
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 Fall '08
 unknown
 Probability, Probability theory, Probability mass function, 5pts

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