The probability that in a year of the 22nd century choosen at random, there will be 53 Sundays is:

$\frac{5}{28}$

The correct answer is Option (3) → $\frac{5}{28}$

Consider a year of 365 days (non-leap) or 366 days (leap year).

Number of weeks = 52 weeks + 1 day (non-leap) or +2 days (leap)

Non-leap year (365 days):

52 full weeks → 52 Sundays guaranteed, 1 extra day → if the extra day is Sunday → 53 Sundays

Probability = 1/7

Leap year (366 days):

52 full weeks → 52 Sundays guaranteed, 2 extra days → if one of the two days is Sunday → 53 Sundays

Probability = 2/7

Number of leap years in 22nd century (2101–2200) = 25 (every 4th year except years divisible by 100 not divisible by 400)

Number of non-leap years = 100 - 25 = 75

Total probability:

$P = \frac{75*(1/7) + 25*(2/7)}{100} = \frac{75+50}{700} = \frac{125}{700} = \frac{5}{28}$

Answer: $\frac{5}{28}$