A leap year has 366 days (52 weeks + 2 days). If a leap year is selected at random, what is the probability that it contains 53 Sundays?

Introduction / Context:In a leap year, two consecutive weekdays occur 53 times. We want the probability that Sunday is one of them.

Given Data / Assumptions:

• 366 days = 52 weeks + 2 extra days.
• Start-of-year weekday is uniform over 7 days.

Concept / Approach:If the year starts on Sunday, both Sunday and Monday occur 53 times. If it starts on Saturday, then Saturday and Sunday occur 53 times. Thus Sunday is 53-times if the start day is Saturday or Sunday.

Step-by-Step Solution:Favorable start days = 2 (Saturday or Sunday).Total start days = 7.Probability = 2/7.

Verification / Alternative check:Matches the standard leap-year weekday distribution logic; compare to ordinary years where only one weekday is 53-times (probability 1/7).

Why Other Options Are Wrong:7/366 and 26/183 are ratios unrelated to weekday-cycle logic; 1/7 holds for ordinary years, not leap years.

Common Pitfalls:Assuming the extra days “belong” to fixed weekdays; they shift with the start day.

Final Answer:2/7