The probability that a leap year selected randomly will have 53 Sundays is

$\frac{2}{7}$

A leap year contain 366 days i.e. 52 weeks and 2 days, clearly there are 52 Sundays in 52 weeks.

For the remaining two days, we may have any of the two days

(i) Sunday and Monday, (ii) Monday and Tuesday, (iii) Tuesday and Wednesday, (iv) Wednesday and Thursday, (v) Thursday and Friday, (iv) Friday and Saturday and (vii) Saturday and Sunday.

Now for 53 Sundays, one of the two days must be Sundays, hence required probability $=\frac{2}{7}.$