AMS310 TEST 1
Form A
PAGE 2 OF 7
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___________________________
Part I: Short answer questions. Very few calculations are required. Write the correct answer in
the space provided by the question number.
_______1.
If there are 12 items in a box, how many samples of n=2 can we choose without
replacement?
Ans))
12
2
12!
66
2!10!
C
=
=
_______2.
P(A) = 0.2 , P(B) = 0.5, P(A
∩
B
)=
0.05.
P(A
∪
B) =____.
Ans))
(
)
(
)
(
)
(
)
P A
B
P A
P B
P A
B
=
+

�
�
=
0.2+0.50.05 = 0.65
________3.
Suppose we toss a single die and the result is the number of dots observed. Then
S={1,2,3,4,5,6}.
Let A= {2,4,6}, and let
B={3 ,4,5,6}.
Then A
∪
B
= __________.
Ans))
{1,2}
B
=
so,
{1,2,4,6}
A
B
=
�
_______4.
P(A)=0.5
P(B)= 0.6, P(A
∩
B) = 0.35
P(BA)=
Ans))
(
)
(

)
(
)
P B
A
P B
A
P A
P
=
0.35
0.7
0.5
=
=
_______5.
Given
S= {1,2,3,4,5,6} the outcomes of the toss of 1 die.
Let A={4,5,6} and let B={1,2,5}.
Which statement below is correct?
(a)
A and B independent events.
A and B are not mutually exclusive events.
(b)
A and B are dependent events. A and B are not mutually exclusive event.
(c)
A and B are independent. A and B are mutually exclusive.
(d) A and B are dependent events. A and B are mutually exclusive.
Ans))
(B)
i)
{5}
A
B
=
�
therefore, A and B are not mutually exclusive.
ii)
1
(
)
2
P A
=
,
1
(
)
2
P B
=
and
1
(
)
({5})
6
P A
B
P
=
=
�
then,
1 1
1
1
(
)
(
)
(
)
2 2
4
6
P A
P B
P A
B
=
=
=
�
�
�
�
Therfore, A and B are dependent events
_______6.
P(AB) =0.1
P(A)=0.2
P(B)=0.6
P(A
∩
B)= ______
Ans))
(
)
(

)
(
)
0.1
0.6
0.06
P A
B
P A B
P B
=
=
=
�
�
�
2