P ROBLEMS FOR THE MIDDLE TERM EXAM
[1] Given three sets
A,B,C
. Use the Venn diagram to illustrate the following sets:
A
∪
B
∪
C
,
A
∩
B
∪
B
∩
(
C
\
(
A
∪
B
))
.
[2] Let a card be selected from two ordinary
packs of 52 cards. Denote
A
=
{
the card is Diamonds or clubs
}
,
B
=
{
the card is a red
suit one
}
, C
=
{
the card is not a Heart Jack
}
.
Compute the following probabilities:
P
(
A
)
,P
(
B
∪
C
)
,P
(
C

B
) [3]
EX 1( 2 points)
: What are a sample space, events an their probilitiy? Formulate
axioms of probability ? Give an example ?
EX 2 ( 2 points)
: What is the conditional probability of an event
A
given
E
.
When three events
A
i
,i
= 1
,
2
,
3 are independent ? Give an example of a sequence of
dependent ( nonindependent) events
A
i
,i
>
3 such that each pair of its membrs are
independent.
EX 3 (2 points)
: A pair of fair dice is tossed. We obtain the ﬁnite equiprobable
Ω consisting of the 36 ordered pairs of numbers between 1 and 6
Ω =
{
(1
,
1)
,
(1
,
2)
,
· · ·
,
(6
,
6)
}
.
Let
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 Spring '09
 thu
 Sets, Probability, Probability theory, ex

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