26. a. Let D = Domestic Equity Fund
P(D) = 16/25 = .64
b. Let A = 4– or 5-star rating
13 funds were rated 3-star of less; thus, 25 – 13 = 12 funds must be 4-star or 5-star.
27. Let A = the event the ACC has a team in the championship game
S = the event the SEC has a team in the championship game
a.
10
( ) .50
20
PA==
b.
8
( ) .40
20
PS ==
1
28. Let: B = rented a car for business reasons
P = rented a car for personal reasons
a. P(B P) = P(B) + P(P) – P(B P)
= .54 + .458 – .30 = .698
b. P(Neither) = 1 – .698 = .302
29. a. P(E) =
1033 .3623
2851 =
P(R) =
854 .2995
2851 =
2851 =
964 .3381
Dividing each entry in the table by 657.0 provides the following joint probability table.
b. Let U = U. S. manufacturer
L = Light Truck
Marginal probabilities: P(U) = .4269 P(B) = .5731
There is a higher probability that the vehicle was not manufactured by a U. S. auto maker. In terms
of market share, non U.S. auto makers lead with a 57.3% share of vehicle sales.
Marginal probabilities: P(C) = .4808 P(L) = .5192
( ) .2939
( ) .4269
( ) .4269
If a vehicle was manufactured by one of the U.S. auto makers, there is a higher probability it will be
in the light truck category.
( ) .3478
( ) .5731
P C N
( ) .2253
( ) .5731
P L N
If a vehicle was not manufactured by one of the U.S. auto makers, there is a higher probability it will
be a car.
( ) .2939
( ) .5192
P U L
If a vehicle was a light truck, there is better than a 50-50 chance that it was manufactured by one of
the U.S. auto makers.
f. There is a higher probability, and thus a larger market share for non U.S. auto makers. However, the
33. a.
Undergraduate Major
Non U.S.
228.5
148.0
376.5
Total
315.9
341.1
657.0
Car
Light Truck
Total
U.S.
.1330
.2939
.4269
Non U.S.
.3478
.2253
.5731
Total
.4808
.5192
1.0000
Business
Engineering
Other
Totals
Intended
Enrollment
Status
Full-Time
.2697
.1510
.1923
.6130
Part-Time
.1149
.1234
.1487
.3870
Totals
.3847
.2743
.3410
1.0000
b. Let B = undergraduate major in business
P(B) = .3847, P(E) = .2743, and P(O) = .3410, so business is the undergraduate major that produces
the most potential MBA students.
c.
P E |F
( )
=P E ÇF
( )
P(F)=.1510
.6130 =.2463
d.
P F |B
( )
=P F ÇB
( )
P(B)=.2697
.3847 =.7012
e. For independence, we must have
P F
( )
P B
( )
=P F ÇB
( )
Given: P(O | J) = .768 P(O | N) = .715 P(O | U) = .822
P(J) = .30 P(N) = .32 P(U) = .38
Joint probabilities using the multiplication law
P(JÇO)=P(J)P(O|J)=(.30)(.768) =.2304
P(UÇO)=P(U)P(O|U)=(.38)(.822) =.3124
On time
Late
Total
Jet Blue
.2304
.0696
.30
United
.2288
.0912
.32
US Airways
.3124
.0676
.38
Total
.7716
.2284
1.00
b. Using the joint probability table, the probability of an on–time flight is the marginal probability
P(O) = .2304 + .2288 + .3124 = .7716
d. From the joint probability table, P(L) = .2284
P(J L)=P(JÇL)
P(L)=.0696
.2284 =.3047
Pay Rent
Yes
No
Yes
.28
.26
.54
Buy a Car
No
.07
.39
.46
.35
.65
b. Let C = the event of financial assistance to buy a car
R = the event of financial assistance to pay rent
c.
( ) .28
( ) .5185
( ) .54
P R C
P R C PC
= = =
.46
()
C
e. Financial assistance to buy a car is not independent of financial assistance to pay rent,
( ) ( )P R C P R
.
f.
( ) ( ) ( ) ( ) .54 .35 .28 .61P C R P C P R P R C = + − = + − =
36. a. Let A = makes 1st free throw
P(AÇB)=P(A)P(B)=(.93)(.93) =.8649
b. At least one shot
P(AÈB)=P(A)+P(B)–P(AÇB)=(.93)+(.93)–.8649 =.9951
c. Miss both
1–P(AÈB)=1–.9951=.0049
d. For the Portland Trail Blazers’ center with P(A) = P(B)= .58
b.
P(E|S)=P(EÇS)
P(S)=.20
.41 =.4878
c.
P(E|D)=P(EÇD)
P(D)=.13
.59 =.2203
d. The probability the worker plans to retire early is greater for the worker who would choose the same
a. From the table,
P(Y)=.42
c.
P(D|Y)=P(DÇY)
P(Y)=.16
.42 =.3810
d.
P(D|N)=P(DÇN)
P(N)=.34
.58 =.5862
e. Individuals who obtained a college degree have a .3810 probability of a delinquent student loan
while individuals who dropped out without obtaining a college degree have a .5862 probability of a
delinquent student loan. Not obtaining a college degree will lead to a greater probability of
.11
2
.03
(A B) .2727
.11
P==
40. a. P(B A1) = P(A1)P(B | A1) = (.20)(.50) = .10
c.
Events
P(Ai)
P(B | Ai)
P(Ai B)
P(Ai | B)
A1
.20
.50
.10
.26
A2
.50
.40
.20
.51
A3
.30
.30
.09
.23
1.00
.39
1.00
(.50)(.75) .375
ParFore should display the special offer that appeals to female visitors.