Chapter 4
Solutions:
1.
Number of experimental Outcomes
=
(3) (2) (4)
=
24
2.
6
3
6!
3 3
6 5 4 3 2 1
3 2 1 3 2 1
20
F
H
G
I
K
J
=
=
⋅ ⋅
⋅
⋅
⋅
⋅
⋅
⋅
⋅
=
! !
(
)(
)
ABC
ACE
BCD
BEF
ABD
ACF
BCE
CDE
ABE
ADE
BCF
CDF
ABF
ADF
BDE
CEF
ACD
AEF
BDF
DEF
3.
P
3
6
6!
6
3
6 5 4
120
=

=
=
(
)!
( )( )( )
BDF
BFD
DBF
DFB
FBD
FDB
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.
5.
P(E
i
) = 1 / 5
for i = 1, 2, 3, 4, 5
P(E
i
)
≥
0
for i = 1, 2, 3, 4, 5
P(E
1
) + P(E
2
) + P(E
3
) + P(E
4
) + P(E
5
) = 1 / 5 + 1 / 5 + 1 / 5 + 1 / 5 + 1 / 5 = 1
The classical method was used.
6.
P
(E
1
) = .40,
P(E
2
) = .26,
P(E
3
) = .34
4  2