This preview shows pages 1–2. Sign up to view the full content.
Steven Weber
Dept. of ECE
Drexel University
ENGR 361: Statistical Analysis of Engineering Systems (Spring, 2008)
Homework 3 (Monday, April 14)
Question 1: Exercise 55,
§
2.4, p75.
Deer ticks can be carriers of either Lyme disease or human granulocytic
ehrlichiosis (HGE). Based on a recent study, suppose that 16% of all ticks in a certain location carry Lyme disease,
10% carry HGE, and 10% of the ticks that carry at least one of these diseases in fact carry both of them. If a
randomly selected tick is found to have carried HGE, what is the probability that the selected tick is also a carrier
of Lyme disease?
Let
A
= carries Lyme disease and
B
= carries HGE. We are told
P
(
A
) = 0
.
16, and
P
(
B
) = 0
.
10, and
P
(
A
∩
B

A
∪
B
) = 0
.
10. Then:
0
.
1 =
P
(
A
∩
B

A
∪
B
) =
P
((
A
∩
B
)
∩
(
A
∪
B
))
P
(
A
∪
B
)
=
P
(
A
∩
B
)
P
(
A
∪
B
)
.
(1)
Next:
P
(
A
∪
B
) =
P
(
A
) +
P
(
B
)

P
(
A
∩
B
) =
P
(
A
) +
P
(
B
)

0
.
1
P
(
A
∪
B
)
.
(2)
Solving this equation yields
P
(
A
∪
B
) = 0
.
236364. Now use
P
(
A
∩
B
) = 0
.
1
P
(
A
∪
B
) = 0
.
02364. Next use
P
(
A

B
) =
P
(
A
∩
B
)
P
(
B
)
= 0
.
02364
/
0
.
1 = 0
.
2364.
Question 2: Exercise 74,
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '04
 Eisenstein

Click to edit the document details