THE UNIVERSITY OF HONG KONG
DEPARTMENT OF STATISTICS AND ACTURIAL SCIENCE
STAT 1301 PROBABILITY AND STATISTICS I
EXAMPLE CLASS 2
1.
A
and
B
are two events. Suppose that
6
.
0
)

(
=
B
A
P
,
3
.
0
)

(
=
A
B
P
and
72
.
0
)
(
=
∪
B
A
P
.
Let
a
A
P
=
)
(
.
(a)
Express
)
(
B
A
P
∩
and
)
(
B
P
in terms of
a
.
(b)
Using the results of (a), or otherwise, find the value of
a
.
(c)
Are
A
and
B
independent events? Explain your answer briefly.
2.
A
and
B
are two events. Suppose that
4
3
)

(
P
=
′
A
B
,
5
3
)

(
P
=
′
B
A
and
5
2
)
(
P
=
′
A
, where
A
′
and
B
′
are
complementary events of
A
and
B
respectively. Let
p
B
=
)
(
P
, where
1
0
<
<
p
.
(a)
Find
)
(
P
B
A
′
∩
.
(b)
Express
)
(
P
B
A
∩
′
in terms of
p
.
(c)
Using the fact that
B
A
∪
′
is the complementary event of
B
A
′
∩
, or otherwise, find the value of
p
.
(d)
Are
A
and
B
mutually exclusive? Explain your answer.
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