$2520=252\times 10$

$=2^2\times 3^2\times 7^1\times 10$

$=2^3\times 3^2\times 5^1\times 7^1$

Number of proper divisors

$=\left(3+1\right)\left(2+1\right)\left(1+1\right)\left(1+1\right)-2$

$=48-2=46$

Number of odd divisors

$=\left(1\right)\left(2+1\right)\left(1+1\right)\left(1+1\right)$,

as power of $2$ should be zero here $=12$

$\bullet$ Subtract $1$ here as in these $12$ divisors, $1$ is also counted which is not included in total proper divisors.

So, probability $=\frac{12-1}{46}$

$=\frac{11}{46}$