What Is the Probability of 53 Sundays and 52 Sundays in a Leap Year?

Learn how to calculate the probability of having 53 Sundays and 52 Sundays in a leap year with a clear explanation of the extra days involved.

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Probability of 53 Sundays in a leap year: 2/7. A leap year has 366 days, so it has 52 weeks and 2 extra days. These extra days can be any pair of consecutive days (e.g., Sunday-Monday, Monday-Tuesday). Since there are 7 possible pairs, each day occurs as one of these extra days 2 times out of 7. Probability of 52 Sundays: Simply 1 - (2/7) = 5/7.

FAQs & Answers

  1. Why does a leap year have 52 weeks and 2 extra days? A leap year has 366 days, which equals 52 full weeks (52 x 7 = 364 days) plus 2 extra days, making the calendar shift by two days each leap year.
  2. How is the probability of 53 Sundays in a leap year calculated? Since the 2 extra days can be any consecutive pair, and Sunday must be one of them to have 53 Sundays, the probability is 2 out of 7, or 2/7.
  3. Can the number of Sundays in a leap year be less than 52? No, a leap year always has at least 52 Sundays because there are 52 full weeks, so the minimum count of any weekday is 52.

Watch More

If you found this explanation helpful, check out our related videos on calculating probabilities for other weekdays in leap and non-leap years, as well as tutorials on calendar-based probability problems.

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