IE 300 / GE 331 Discussion Problem Set 1
•
217 (Sample space and events) Describe both the sample space and the event “
at most four calls are needed to
get connected”
c = connected, b = busy,
S = {c, bc, bbc, bbbc, bbbbc, …}, E={c, bc, bbc, bbbc}
•
219 (e) (Venn diagram)
•
(Event operations) The sample space of a random experiment is
S={1,2,3,.
..,10}
.
Three events
A, B
and
C
are
such that
A
∩
B={3,4,5}, A
U
B={1,2,3,4,5}, C={4,5,6}.
What are
A
’
U
B
’,
A
’
∩
B
’
and
(A
∩
C)
U
(B
∩
C)
?
By DeMorgan’s laws,
},
10
,
9
,
8
,
7
,
6
,
2
,
1
{
)'
(
'
'
=
=
B
A
B
A
I
U
}.
10
,
9
,
8
,
7
,
6
{
)'
(
'
'
=
=
B
A
B
A
U
I
By Distributive law,
( 29 ( 29 ( 29
{1,2,3,4,5} {4,5,6} {4,5}
A
C
B
C
A
B
C
=
=
=
I
U
I
U
I
I
•
242 (Counting)
a)
If the chips are of different types, then every arrangement of 5 locations selected from the 12
results in a different layout. Therefore,
040
,
95
!
7
!
12
12
5
=
=
P
layouts are possible.
b)
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 Spring '09
 NegarKayavash
 Probability theory, Natural number, Discussion Problem Set

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