ALL CHAPTERS COVERED
,2.1
TAB TBC CAB CBC TAC CAC
6 2 1200 300 8 1500
3 300 9 1500
7 2 1200 300 9 1500
3 300 10 1500
9 2 550 300 11 850
3 300 12 850
10 2 550 300 12 850
3 300 13 850
11 2 550 300 13 850
3 300 14 850
(a) Sample space of travel time from A to B = {6, 7, 9, 10, 11}
Sample space of travel time from A to C = {8, 9, 10, 11, 12, 13, 14}
(b) Sample space of travel cost from A to C = {850, 1500}
(c) Sample space of TAC and CAC
= {(8, 1500), (9, 1500), (10, 1500), (11, 850), (12, 850), (13, 850), (14, 850)}
,2.2
(a) Since the possible values of settlement for Pier 1 overlap partially with those of Pier 2, it is
possible that both Piers will have the same settlement. Hence, the minimum differential
settlement is zero.
The maximum differential settlement will happen when the settlement of Pier 2 is 10 cm and
that of Pier 1 is 2 cm, which yields a differential settlement of 8 cm.
Hence, the sample space of the differential settlement is zero to 8 cm.
(b) If the differential settlement is assumed to be equally likely between 0 and 8 cm, the
probability that it will be between 3 and 5 cm is equal to
5−3 2
P= = = 0.25
8−0 8
, 2.3
(a)
(b)
Wind
direction
E1
90o E2
E3
60o
E1
30o
Wind Speed
0 15 35 45
(c)
A and B are not mutually exclusive
A and C are not mutually exclusive
,2.1
TAB TBC CAB CBC TAC CAC
6 2 1200 300 8 1500
3 300 9 1500
7 2 1200 300 9 1500
3 300 10 1500
9 2 550 300 11 850
3 300 12 850
10 2 550 300 12 850
3 300 13 850
11 2 550 300 13 850
3 300 14 850
(a) Sample space of travel time from A to B = {6, 7, 9, 10, 11}
Sample space of travel time from A to C = {8, 9, 10, 11, 12, 13, 14}
(b) Sample space of travel cost from A to C = {850, 1500}
(c) Sample space of TAC and CAC
= {(8, 1500), (9, 1500), (10, 1500), (11, 850), (12, 850), (13, 850), (14, 850)}
,2.2
(a) Since the possible values of settlement for Pier 1 overlap partially with those of Pier 2, it is
possible that both Piers will have the same settlement. Hence, the minimum differential
settlement is zero.
The maximum differential settlement will happen when the settlement of Pier 2 is 10 cm and
that of Pier 1 is 2 cm, which yields a differential settlement of 8 cm.
Hence, the sample space of the differential settlement is zero to 8 cm.
(b) If the differential settlement is assumed to be equally likely between 0 and 8 cm, the
probability that it will be between 3 and 5 cm is equal to
5−3 2
P= = = 0.25
8−0 8
, 2.3
(a)
(b)
Wind
direction
E1
90o E2
E3
60o
E1
30o
Wind Speed
0 15 35 45
(c)
A and B are not mutually exclusive
A and C are not mutually exclusive
