The probability that a year chosen at random has 53 Sundays is

The probability of 53 Sundays is $\frac{1}{7}$ for non leap year and $\frac{2}{7}$ for leap year.

$\therefore$Required Probability$=\frac{3}{4}\cdot \frac{1}{7}+\frac{1}{47}\cdot \frac{2}{7}=\frac{5}{28}$