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MAA AMC
AMC 12/AHSME
1990 AMC 12/AHSME
18
Random Integers
Random Integers
Source:
April 4, 2006
probability
Problem Statement
First
a
a
a
is chosen at random from the set
{
1
,
2
,
3
,
…
,
99
,
100
}
\{1,2,3,\ldots,99,100 \}
{
1
,
2
,
3
,
…
,
99
,
100
}
, and then
b
b
b
is chosen at random from the same set. The probability that the integer
3
a
+
7
b
3^a+7^b
3
a
+
7
b
has units digit
8
8
8
is
(A)
1
16
(B)
1
8
(C)
3
16
(D)
1
5
(E)
1
4
\text{(A)} \ \frac1{16} \qquad \text{(B)} \ \frac18 \qquad \text{(C)} \ \frac{3}{16}\qquad \text{(D)} \ \frac15 \qquad \text{(E)} \ \frac14
(A)
16
1
(B)
8
1
(C)
16
3
(D)
5
1
(E)
4
1
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