In a non-leap year (365 days), what is the probability that the year contains exactly 52 Tuesdays (i.e., not 53 Tuesdays)?
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A1/7
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B2/7
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C3/7
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D6/7
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ENone of these
Answer
Correct Answer: 6/7
Explanation
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:
Total possible “extra weekdays” = 7.Favorable choices (extra day is not Tuesday) = 6.Probability = 6/7.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