In a non-leap year (365 days), what is the probability that the year contains exactly 52 Tuesdays (i.e., not 53 Tuesdays)?

Introduction / Context:A non-leap year has 365 days = 52 full weeks + 1 extra day. Thus each weekday occurs 52 times, and one weekday (the weekday of January 1) occurs a 53rd time. We need exactly 52 Tuesdays, so the extra day must NOT be Tuesday.

Given Data / Assumptions:

• Non-leap year: 365 days.
• Exactly one extra day beyond 52 weeks.
• Start weekday is equally likely among 7 days (assuming a random model across years).

Concept / Approach:There are 7 equally likely choices for which weekday occurs 53 times. Exactly 52 Tuesdays means Tuesday is not the extra weekday. Therefore probability = 6/7.

Step-by-Step Solution:

Verification / Alternative check:If the extra day is Tuesday, there are 53 Tuesdays; in the other six cases there are exactly 52 Tuesdays. Hence 6 of 7 outcomes are favorable.

Why Other Options Are Wrong:1/7 is the probability of 53 Tuesdays; 2/7 and 3/7 are not consistent with the single extra-day structure.

Common Pitfalls:Confusing “at least 52” with “exactly 52”, or applying leap-year logic (366 days) by mistake.

Final Answer:6/7