STAT 400 / MATH 463
Fall 2011
Homework #1
(due Friday, September 2, by 3:00 p.m.)
No credit will be given without supporting work.
1.
Suppose that
P
(
A
)
= 0.60,
P
(
B
)
= 0.40,
P
(
A
B
)
= 0.30.
What is the probability that …
a)
either A occurs or B occurs (or both);
b)
B does not occur;
c)
B occurs and A does not occur;
d)
neither A nor B occurs.
2.
Suppose
P
(
A
)
= 0.6,
P
(
B
)
= 0.5,
P
(
C
)
= 0.4,
P
(
A
B
)
= 0.3,
P
(
A
C
)
= 0.2,
P
(
B
C
)
= 0.2,
P
(
A
B
C
)
= 0.1.
Find …
a)
P
(
A
B
)
;
b)
P
(
B
C
)
;
c)
P
(
(
A
B
)
C
'
)
;
d)
P
(
A
(
B
C
)
)
.
3.
Suppose a baseball player steps to the plate with the intention of trying to
“coax” a base on balls by never swinging at a pitch.
The umpire, of course,
will necessarily call each pitch either a ball (B) or a strike (S).
What outcomes
make up the event A, that a batter walks on the sixth pitch?
Note:
A batter
“walks” if the fourth ball is called before the third strike.
4.
Consider a “thick” coin with three possible outcomes of a toss
(
Heads
,
Tails
,
and
Edge
)
for which
Heads
and
Tails
are equally likely,
but
Edge
is seven
times less likely than
Heads
.
What is the probability of
Heads
?
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