York University
MATH 2030 3.0AF (Elementary Probability)
Midterm I  SOLUTIONS
October 12, 2007
NAME:
STUDENT NUMBER:
You have 50 minutes to complete the examination.
There are 5 questions on
4 pages.
You may bring one lettersized twosided formula sheet to the exam.
No other books or notes may be used.
You may use a calculator.
Show all
your work, and explain or justify your solutions to the extent possible. You may
leave numerical answers or binomial coefficient unsimplified, unless specifically
told otherwise. Use the back of your page if you run out of room.
1. [10]
P
(
A
) = 0
.
3 and
P
(
B
) = 0
.
2; What value of
P
(
A
∪
B
) ensures that
(a)
A
and
B
are independent?
(b)
A
and
B
are disjoint?
Solution:
(a) If
A
and
B
are independent then
P
(
A
∪
B
) =
P
(
A
) +
P
(
B
)

P
(
A
∩
B
) =
P
(
A
) +
P
(
B
)

P
(
A
)
P
(
B
) = 0
.
3 + 0
.
2

0
.
3
×
0
.
2 = 0
.
44
(b) If
A
and
B
are disjoint then
P
(
A
∪
B
) =
P
(
A
) +
P
(
B
) = 0
.
3 + 0
.
2 = 0
.
5
2. [10] Suppose
P
(
A
) = 0
.
4,
P
(
B
) = 0
.
2, and
P
(
A

B
) = 0
.
7
Find
P
(
A
∩
B
c
).
Solution:
P
(
A
∩
B
c
) =
P
(
A
)

P
(
A
∩
B
) =
P
(
A
)

P
(
B
)
P
(
A

B
) = 0
.
4

0
.
2
×
0
.
7 = 0
.
26
3. You are dealt 10 cards from a regular deck of 52 cards.
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 Winter '09
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 Conditional Probability, Probability, Amit, Betsy –

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