MATH 3081 Homework 5 .
Name:
3.2.4 An entrepreneur owns six corporations, each with more than $10 million in assets. The entrepreneur consults the
U.S. Internal Revenue Data Book and discovers that the IRS audits 15.3% of businesses of that size. What is the
probability that two or more of these businesses will be audited?
C
more) &
n = G PlAudit Cor more) + P(Auditz or =
more)
p(Ardit
2 or
:.
153 1. p[Ardit 1) -
p(Audito) =
p
1 ,2
1) binpdf (6 153 01) =
P(Audit or worel
(binpdf[6 153
..
:
X + ,
I -
.. ,
=
.
231 =
O 23 1 %
.
3.2.7 Doomsday Airlines (“Come Take the Flight of Your Life”) has two dilapidated airplanes, one with two engines,
and the other with four. Each plane will land safely only if at least half of its engines are working. Each engine on
each aircraft operates independently and each has probability p = 0.4 of failing. Assuming you wish to maximize
your survival probability, which plane should you fly on?
PCLive) :
p(2 or more engine 2
= ↑
PCLive) p(lor engine) n : 2
:. Y
: more
p
P =. 4
1 -
P(0) = p(live)
pllive) = /- p(d) 4 0) 87
1-binpdf (4 , . ,
=.
I-binpdf (2 4 0) =. 64
give
=
.. ,
ble 87 % of living
plane
3.2.8 Two lighting systems are being proposed for an employee work area. One requires fifty bulbs, each having a
probability of 0.05 of burning out within a months time. The second has one hundred bulbs, each with a 0.02
burnout probability. Whichever system is installed will be inspected once a month for the purpose of replacing
burned-out bulbs. Which system is likely to require less maintenance? Answer the question by comparing the
probabilities that each will require at least one bulb to be replaced at the end of thirty days.
n = 50 piloc less maintenance
02
Pi .
05 n =.
o a
PCat least (bulb) = 1-biapdf (50 ,.
05 ,
Platleast (bulb) :
1-binpdf
(100 .
02 ,
= 92 3 % it needs %
= 86 7
replacing
.
.
replacing
3.2.9 The great English diarist Samuel Pepys asked his friend Sir Isaac Newton the following question: Is it more likely
to get at least one 6 when six dice are rolled, at least two 6s when twelve dice are rolled, or at least three 6’s when
eighteen dice are rolled? After considerable correspondence [see (158)]. Newton convinced the skeptical Pepys
that the first event is the most likely. Compute the three probabilities. Newton is
always right
nies
12
18
n = n :
L-binpdf (6 ,
" e
p : TG p
:
G
I
/ q 3
q 9:
= 2 > :
O66 3 1 p(x) p(i) p(d) p() p()
-
- - -
.
1 -
1- 112 - 764 135 .. 23
1
.
0376
. -
-
·
.
.
=
Co
. % 59 7
Name:
3.2.4 An entrepreneur owns six corporations, each with more than $10 million in assets. The entrepreneur consults the
U.S. Internal Revenue Data Book and discovers that the IRS audits 15.3% of businesses of that size. What is the
probability that two or more of these businesses will be audited?
C
more) &
n = G PlAudit Cor more) + P(Auditz or =
more)
p(Ardit
2 or
:.
153 1. p[Ardit 1) -
p(Audito) =
p
1 ,2
1) binpdf (6 153 01) =
P(Audit or worel
(binpdf[6 153
..
:
X + ,
I -
.. ,
=
.
231 =
O 23 1 %
.
3.2.7 Doomsday Airlines (“Come Take the Flight of Your Life”) has two dilapidated airplanes, one with two engines,
and the other with four. Each plane will land safely only if at least half of its engines are working. Each engine on
each aircraft operates independently and each has probability p = 0.4 of failing. Assuming you wish to maximize
your survival probability, which plane should you fly on?
PCLive) :
p(2 or more engine 2
= ↑
PCLive) p(lor engine) n : 2
:. Y
: more
p
P =. 4
1 -
P(0) = p(live)
pllive) = /- p(d) 4 0) 87
1-binpdf (4 , . ,
=.
I-binpdf (2 4 0) =. 64
give
=
.. ,
ble 87 % of living
plane
3.2.8 Two lighting systems are being proposed for an employee work area. One requires fifty bulbs, each having a
probability of 0.05 of burning out within a months time. The second has one hundred bulbs, each with a 0.02
burnout probability. Whichever system is installed will be inspected once a month for the purpose of replacing
burned-out bulbs. Which system is likely to require less maintenance? Answer the question by comparing the
probabilities that each will require at least one bulb to be replaced at the end of thirty days.
n = 50 piloc less maintenance
02
Pi .
05 n =.
o a
PCat least (bulb) = 1-biapdf (50 ,.
05 ,
Platleast (bulb) :
1-binpdf
(100 .
02 ,
= 92 3 % it needs %
= 86 7
replacing
.
.
replacing
3.2.9 The great English diarist Samuel Pepys asked his friend Sir Isaac Newton the following question: Is it more likely
to get at least one 6 when six dice are rolled, at least two 6s when twelve dice are rolled, or at least three 6’s when
eighteen dice are rolled? After considerable correspondence [see (158)]. Newton convinced the skeptical Pepys
that the first event is the most likely. Compute the three probabilities. Newton is
always right
nies
12
18
n = n :
L-binpdf (6 ,
" e
p : TG p
:
G
I
/ q 3
q 9:
= 2 > :
O66 3 1 p(x) p(i) p(d) p() p()
-
- - -
.
1 -
1- 112 - 764 135 .. 23
1
.
0376
. -
-
·
.
.
=
Co
. % 59 7
