UNIVERSITY OF VICTORIA
MATHEMATICS 151, SECTION A02, FALL 2008
SITDOWN PRACTICE TEST 2, NOVEMBER 19
Question 1.
You roll a fair 4 sided die twice and multiply the numbers showing on the top face of
each roll. What is the expected value of this experiment? (The numbers on the faces of a 4
sided die are 1
,
2
,
3, and 4).
(A)
0
(B)
1
(C)
2
(D)
3
(E)
4
(F)
5
(G)
6
(H)
7
(I)
8
(J)
9
Solution:
The possible results of two rolls can be summarized by the following table:
1
2
3
4
1
1
2
3
4
2
2
4
6
8
3
3
6
9
12
4
4
8
12
16
Each of these occurs with probability
1
16
, and so summing up we find that the expected value
is
100
16
= 6
.
25. So the answer is (G).
Question 2.
There is a game where the player flips a fair coin 6 times. If they get exactly 2 heads
they must pay $4.
If they get exactly 3 heads, they receive $4, and if they get exactly 4
heads they receive $12. Otherwise, they get and pay nothing. How much should they expect
to win on average by playing this game repeatedly?

$4(
P
(
X
= 2)) + $4(
P
(
X
= 3)) + $12(
P
(
X
= 4))
=

$4
6
2
(0
.
5)
2
(0
.
5)
4
+ $4
6
3
(0
.
5)
3
(0
.
5)
3
+ $12
6
4
(0
.
5)
4
(0
.
5)
2
=

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 Spring '11
 stephenlang
 Math, Calculus, Addition, Following

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