October 12, 2009
MATH 230 HOMEWORK # 1
(Due: October 20, 2009, Tuesday)
[Please, submit your homework to my office (SA 105) by 5:30 PM]
(DO NOT forget to write your Section number)
1.
There are
2
boxes, each has
r
balls numbered from
1
through
r
.
A random sample of n
balls is
drawn
(
r
n
≤
)
without replacement from each box. Find the probability that the samples
contain exactly
k
having the same numbers in common.
2.
Let
A
1,
A
2
and
B
1
, B
2
events such that
5
.
0
)
(
)
(
1
1
=
=
B
P
A
P
and
6
.
0
)
(
1
2
=
A
A
P
,
4
.
0
)
(
1
2
=
A
B
P
,
4
.
0
)
(
1
2
=
B
A
P
,
6
.
0
)
(
1
2
=
B
B
P
. Show that
5
.
0
)
(
)
(
2
2
=
=
B
P
A
P
3.
Consider the experiment of rolling two dice. Define the events A, B, C so that
A= {First die results in a 1, 2, or 3}
B= {second die results in a 4, 5, or 6}
C= {The sum of two faces is 7}
Show that A, B and C are pairwise independent but not (mutually) independent.
4.
In a customer satisfaction survey,
5
3
of those surveyed had a Japanesemade car,
10
3
Europeanmade car, and
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 Fall '10
 DILEKGüVENç
 Probability theory, #, 40%, 10 digits, $90 000

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