MAT2378B: Assignment 1
Due date: 07 October 2009
Total number of points: 34
Q
1.
The three events are shown on the Venn diagram:
’$
A
’$
B
’$
C
Reproduce the ﬁgure and shade the region corresponding to the following events:
(a)
A
c
(b)
(
A
and
B
) or (
A
and
B
c
)
(c)
(
A
and
B
) or
C
(d)
(
B
or
C
)
c
(e)
(
A
and
B
)
c
and
C
Solution to Q1:
Marking scheme for Q1:
Correct answer for each part  1 point. Total  5 points.
Q
2.
(Q3.5) In a certain college, 55% of the students are women. We take a sample of two students. Find the
probability that
(a)
both are women;
(b)
at least on of the two students is a woman.
Solution to Q2:
(a)
0
.
55
×
0
.
55 = 0
.
3025
(b)
0
.
55
×
0
.
55 + 0
.
45
×
0
.
55 + 0
.
45
×
0
.
55 = 0
.
7975
Marking scheme for Q2:
Correct answer for each part  1 point. Total  2 points.
Q
3.
If
P
(
A
) = 0
.
3,
P
(
B
) = 0
.
2, and
P
(
A
and
B
) = 0
.
1, determine the following probabilities:
(a)
P
(
A
c
)
(b)
P
(
A
or
B
)
(c)
P
(
A
c
and
B
)
(d)
P
(
A
and
B
c
)
(e)
P
((
A
or
B
)
c
)
(f)
P
(
A
c
or
B
)
Solution to Q3:
(a)
P
(
A
c
) = 1

P
(
A
) = 0
.
7
(b)
P
(
A
or
B
) =
P
(
A
) +
P
(
B
)

P
(
A
and
B
) = 0
.
4
(c)
P
(
A
c
and
B
) =
P
(
B
)

P
(
A
and
B
) = 0
.
1 (draw a Venn diagram to see this)
(d)
P
(
A
and
B
c
) =
P
(
A
)

P
(
A
and
B
) = 0
.
2
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P
((
A
or
B
)
c
) = 1

P
(
A
or
B
) = 1

0
.
4 = 0
.
6
(f)
P
(
A
c
or
B
) =
P
(
A
c
) +
P
(
B
)

P
(
A
c
and
B
) = 0
.
7 + 0
.
2

0
.
1 = 0
.
8
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 Spring '09
 ALYAOTHMAN

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