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You choose an integer n at random in the interval 1 <= n <= 100.  What is the probability that the fraction n/162 is reducible?

 May 11, 2020
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Count them. I counted 67 fractions that are reducible:

 

1 / 162
1 / 81
1 / 54
2 / 81
5 / 162
1 / 27
7 / 162
4 / 81
1 / 18
5 / 81
11 / 162
2 / 27
13 / 162
7 / 81
5 / 54
8 / 81
17 / 162
1 / 9
19 / 162
10 / 81
7 / 54
11 / 81
23 / 162
4 / 27
25 / 162
13 / 81
1 / 6
14 / 81
29 / 162
5 / 27
31 / 162
16 / 81
11 / 54
17 / 81
35 / 162
2 / 9
37 / 162
19 / 81
13 / 54
20 / 81
41 / 162
7 / 27
43 / 162
22 / 81
5 / 18
23 / 81
47 / 162
8 / 27
49 / 162
25 / 81
17 / 54
26 / 81
53 / 162
1 / 3
55 / 162
28 / 81
19 / 54
29 / 81
59 / 162
10 / 27
61 / 162
31 / 81
7 / 18
32 / 81
65 / 162
11 / 27
67 / 162
34 / 81
23 / 54
35 / 81
71 / 162
4 / 9
73 / 162
37 / 81
25 / 54
38 / 81
77 / 162
13 / 27
79 / 162
40 / 81
1 / 2
41 / 81
83 / 162
14 / 27
85 / 162
43 / 81
29 / 54
44 / 81
89 / 162
5 / 9
91 / 162
46 / 81
31 / 54
47 / 81
95 / 162
16 / 27
97 / 162
49 / 81
11 / 18
50 / 81
If my count is correct, then the probability is =67/100 =2/3

 May 11, 2020

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