The probability that a leap year selected at random contains either 53 Sundays or 53 Mondays, is:

Total number of days in a leap year = 366

It will contain 52 weeks and 2days

These two days can be (Sunday, Monday); (Monday, Tuesday); (Tuesday, Wednesday); (Wednesday, Thursday); (Thursday, Friday); (Friday, Saturday); (Saturday, Sunday)

For 53 Sundays, probability = $$\ \ \frac{2}{7}$$

Similarly for 53 Mondays, probability =$$\ \ \frac{2}{7}$$

This includes one way where Sunday and Monday occur simultaneously (i.e) Sunday, Monday 

Probability for this =$$\ \ \frac{1}{7}$$

Hence required probability = $$\ \ \frac{2}{7}$$ +$$\ \ \frac{2}{7}$$-$$\ \ \frac{1}{7}$$

=$$\ \ \frac{3}{7}$$

C is the correct answer.