STA 4321/5325
Quiz 2
Name:
KEY
Mathematical Statistics 1
Fall 2008
UF ID:
1.
In responding to survey questions which concern sensitive topics people may not respond
truthfully. Suppose that we plan to survey 12th graders and ask “Have you tried marijuana?”
Assume that 40% of 12th graders who have tried marijuana will lie and respond “no”, and
that 10% of those who have not tried marijuana will lie and respond “yes”. Assume also that
55% of all 12th graders have actually tried marijuana. A 12th grader is selected at random.
(a) What is the probability that the person selected will answer “yes” to the question?
(SET UP ONLY)
(5 pts)
M
=
{
has tried marijuana
}
Y
=
{
answers yes
}
N
=
{
answers no
}
=
Y
P
(
N

M
) =
.
40 =
⇒
P
(
Y

M
) =
.
60
P
(
Y

M
) =
.
10
P
(
M
) =
.
55 =
⇒
P
(
M
) =
.
45
P
(
Y
) =
P
(
M
)
P
(
Y

M
) +
P
(
M
)
P
(
Y

M
) =
(
.
55)(
.
60) + (
.
45)(
.
10)
= 0
.
375
(b) If the person selected answers “yes,” what is the probability that the person has actually
tried marijuana? (SET UP ONLY)
(5 pts)
P
(
M

Y
) =
P
(
M
∩
Y
)
P
(
Y
)
=
P
(
M
)
P
(
Y

M
)
P
(
M
)
P
(
Y

M
) +
P
(
M
)
P
(
Y

M
)
=
(
.
55)(
.
60)
(
.
55)(
.
60) + (
.
45)(
.
10)
=
.
33
.
375
=
.
88
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STA 4321/5325
Quiz 2
2
2.
An electrical circuit is composed of relays of types A, B, and C in the configuration pic
tured below. Suppose that individual relays of types A, B, and C function properly with
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