Name _______________________
Closed book and notes. 60 minutes.
1. True or false. (3 points each)
(a)
T
←
F
If
A
is an event, then
A
and
A
′
are mutually exclusive.
(b)
T
←
F
If
A
is an event, then
A
and
A
′
partition the sample space.
(c)
T
F
←
If P(
A

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

A
)
=
P(
A
).
(e)
T
←
F
If
∅
denotes the empty set, then P(
∅
)
=
0.
(f)
T
F
←
If
A
and
B
are events, then P(
A

B
)
≥
P(
A
).
(g)
T
F
←
If
A
is an event, then P(
A

A
∪
A
′
)
=
0.
(h)
T
←
F
If
A
and
B
are
positiveprobability
events,
then
P(
A

B
) P(
B
)
=
P(
B

A
) P(
A
).
(i)
T
F
←
If
A
and
B
are events and
A
is a subset of
B
, then P(
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
diamonds are red.
Consider the experiment of choosing ten cards without replacement.
For draw
i
=
1, 2,.
.., 10, let
Q
i
denote that a queen is chosen, let
K
i
denote that a king is chosen,
and let
A
i
denote that an ace is chosen.
(a) (3 points) T