Name ___ < KEY > ___
Closed book and notes. 60 minutes.
1. True or false. (3 points each)
(a)
T
←
F
If
S
is the sample space of an experiment, then P(
S
′
)
=
0.
(b)
T
←
F
If
A
and
B
are events, then P(
A
∩
B
)
≤
P(
A
).
(c)
T
←
F
If
E
1
,
E
2
,...,
E
n
partition
the
sample
space
S
,
then
E
1
∪
E
2
∪
. . .
∪
E
n
=
S
.
(d)
T
F
←
If P(
A

B
)
=
0.7, P(
B
)
=
0.4, and P(
A
)
=
0.7, then
B
′
and
A
′
are
mutually exclusive.
(e)
T
F
←
If
A
is an event, then
A
and
A
′
are independent.
(f)
T
F
←
If events
A
and
B
are independent, then
A
and
B
partition the sample
space.
(g)
T
F
←
If P(
A

B
)
=
0.5, P(
B
)
=
0.5, and P(
A
′
)
=
0.3, then
B
′
and
A
′
are
independent.
(h)
T
←
F
If
A
and
B
are independent events, then P(
B
′

A
)
=
P(
B
′
).
(i)
T
←
F
If the event
A
is a subset of
B
, then P(
A

B
)
≥
P(
A
).
2. Recall: A 52card deck has four suits (spades, hearts, diamonds, and clubs) and thirteen
values (Ace, 2, 3,.
..,10, Jack, Queen, and King). Spades and clubs are black; hearts and