Introduction to Probability
Chapter 4
Introduction to Probability
Solutions:
4.
a.
H
T
H
T
H
T
H
T
H
T
H
T
H
T
(H,H,H)
(H,H,T)
(H,T,H)
(H,T,T)
(T,H,H)
(T,H,T)
(T,T,H)
(T,T,T)
1st Toss
2nd Toss
3rd Toss
b.
Let: H be head and T be tail
(H,H,H) (T,H,H)
(H,H,T) (T,H,T)
(H,T,H) (T,T,H)
(H,T,T) (T,T,T)
c.
The outcomes are equally likely, so the probability of each outcomes
is 1/8.
6.
P
(E
1
) = .40,
P
(E
2
) = .26,
P
(E
3
) = .34
The relative frequency method was used.
7.
No.
Requirement (4.4) is not satisfied; the probabilities do not sum
to 1.
P
(E
1
) +
P
(E
2
) +
P
(E
3
) +
P
(E
4
) = .10 + .15 + .40 + .20 = .85
11.
a.
Total drivers = 858 + 228 = 1086
P
(Seatbelt) =
858
.79
1086
=
or 79%
b.
Yes, the overall probability is up from .75 to .79, or 4%, in one year.
Thus .79 does exceed his .78 expectation.
c.
Northeast
148
.74
200
=
Midwest
162
.75
216
=
South
296
.80
370
=
West
252
.84
300
=
The West with .84 shows the highest probability of use.
d.
Probability of selection by region:
Northeast
200
.184
1086
=
Midwest
216
.200
1086
=
South
370
.340
1086
=
West
300
.286
1086
=
South has the highest probability (.34) and West was second (.286).
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