Test Index

Probability Part 2

Section: Mathematics

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Question : 58 of 100

Marks: +1, -0

Let

S=\{1,2,3,\dots,2022\}

. Then the probability, that a randomly chosen number

n

S

\text{HCF}(n,2022)=1

[29-Jul-2022-Shift-1]

$\; \frac{128}{1011}$
$\; \frac{166}{1011}$
$\; \frac{127}{337}$
$\; \frac{112}{337}$

Solution:

S=\{1,2,3,\dots,2022\}

\text{HCF}(n,2022)=1

\Rightarrow n

and 2022 have no common factor

Total elements

=2022

2022=2 \times 3 \times 337

M

: numbers divisible by 2.

\{2,4,6,\dots,2022\} \;\; n(M)=1011

N

: numbers divisible by 3.

\{3,6,9,\dots,2022\} \;\; n(N)=674

L

: numbers divisible by 6 .

\{6,12,18,\dots,2022\} \;\; n(L)=337

n(M \cup N)=n(M)+n(N)-n(L)

=1011+674-337

=1348

0=

Number divisible by 337 but not in

M \cup N

\{337,1685\}

Number divisible by 2,3 or 337

=1348+2=1350

Required probability

=\; \frac{2022-1350}{2022}

=\; \frac{672}{2022}

=\; \frac{112}{337}

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