STAT 408
Spring 2009
Homework #1
(due Friday, January 30, by 3:00 p.m.)
1.
Suppose that
P(A) = 0.40,
P(B) = 0.30,
P(A
∩
B) = 0.20.
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;
a)
P
(
A
∪
B
) =
0.50
.
b)
P
(
B
'
) =
0.70
.
c)
P
(
B
∩
A
'
) =
0.10
.
d)
P
(
A
'
∩
B
'
) =
0.50
.
2.
Let events A and B and sample space S be defined as the following intervals:
S =
{
x
: 0
≤
x
≤
10
}
,
A =
{
x
: 0 <
x
< 5
}
,
B =
{
x
: 3
≤
x
≤
7
}
.
Characterize the following events:
a)
A
'
b)
A
∩
B
c)
A
∪
B
{
0
}
∪
[
5, 10
]
[
3, 5
)
(
0, 7
]
d)
A
∩
B
'
e)
A
'
∪
B
f)
A
'
∩
B
'
(
0, 3
)
{
0
}
∪
[
3, 10
]
{
0
}
∪
(
7, 10
]
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View Full Document3.
An urn contains six chips numbered 1 through 6.
Three are drawn out.
What
outcomes are in the event “Second smallest chip is a 3”?
Assume that the order
of the chips is irrelevant.
(
1, 3, 4
)
(
1, 3, 5
)
(
1, 3, 6
)
(
2, 3, 4
)
(
2, 3, 5
)
(
2, 3, 6
)
4.
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?
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 Spring '08
 STEPANOV
 Statistics, Probability, HTHT HTTH HTTT, THHT THTH THTT, THTH THTT TTHH, TTHT TTTH TTTT

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