Let S = {1,2,3,... ,2022}. Then the probability that a randomly chosen number n from the set S such that HCF (n, 2022) = 1, is :

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

$\frac{128}{1011}$

$\frac{112}{337}$

$\frac{166}{1011}$

$\frac{127}{337}$

answer is D.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

$S = {1, 2, 3, \dots . ., 2022}, HCF (n, 2022) = 1 2022 = 2 \times 3 \times 337$

Numbers which are divisible by 2 are 2, 4, ....2022 i.e.,l0ll
Numbers which are divisible by 3 are 3, 6,9 ....2022 i.e.,674
Numbers which are divisible by 6 are 6, 12, ....2022 i.e.,337
Numbers which are divisible by 337 arc 337,6?4, ..-. 2022, i.e.,6
Numbers which are divisible by 2 x 337 are 674,1348,2022. i.e.,3
Numbers which are divisible by 3 x 337 are l0ll,2022. i.e-,2
Numbers which are divisible by 2022 are 2022. i.e., 1
$∴$ Total numbers which are divisible by 2 or 3 or 337
$= 1011 + 674 + 6 - 337 - 3 - 2 + 1 = 1692 - 342 = 1350$
For HCF (n, 2022) = 1, we have numbers of elements for n=2O22-1150=672
$∴$ Required probability $= \frac{672}{2022} = \frac{112}{337}$