Let \( S=\{1,2,3, \ldots, 2022\} \). Then the probability, that a randomly chosen number \( n \)...

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Let \( S=\{1,2,3, \ldots, 2022\} \). Then the probability, that a randomly chosen number \( n \) from the set \( S \) such that HCF \( (n, 2022)=1 \), is:
(a) \( \frac{128}{1011} \)
(b) \( \frac{166}{1011} \)
(c) \( \frac{127}{337} \)
(d) \( \frac{112}{337} \)
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