What Is the Probability of Getting 5 Sundays in a 31-Day Month?

Learn why the probability of having 5 Sundays in any 31-day month is 1/7, based on the distribution of days in a week.

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The probability of getting 5 Sundays in a 31-day month (January, March, May, July, August, October, or December) is 1/7. This is because there are 7 days in a week, and a 31-day month will have 4 weeks and 3 extra days. For a month to have 5 Sundays, one of these 3 extra days needs to be a Sunday.

FAQs & Answers

  1. Why is the probability of 5 Sundays in a 31-day month exactly 1/7? Because there are 7 days in a week and 3 extra days beyond 4 full weeks in a 31-day month, one of those extra days must be Sunday for there to be 5 Sundays, making the chance 1 out of 7.
  2. Which months have 31 days and can have 5 Sundays? The months with 31 days are January, March, May, July, August, October, and December, and any of these can have 5 Sundays depending on the day the month starts.
  3. How often do months have 5 Sundays in a year? On average, months with 31 days have a 1/7 chance of containing 5 Sundays, so typically a few months each year will have 5 Sundays depending on the calendar year.

Watch More

Explore more about calendar probabilities and date-related calculations in our related videos, including how many weekends a month can have and the likelihood of specific weekdays appearing multiple times.

  1. What Is the Probability of Getting 5 Sundays in a 31-Day Month? Learn how to calculate the probability of having 5 Sundays in a 31-day month and what calendar start days affect this frequency.
  2. What Is the Probability of January Having 5 Sundays? Learn why January has a 1 in 7 chance of containing 5 Sundays based on the month's start day and length.
  3. What is the Probability of Having 5 Sundays in January? Learn how to calculate the probability of 5 Sundays in January and why it happens about 42.86% of the time.
  4. What Is the Probability of Getting 5 Sundays in a 30-Day Month? Learn why the probability of having 5 Sundays in a 30-day month is zero and understand the calendar calculation behind it.
  5. What Is the Probability of Having 5 Sundays in a Month? Discover how often months with 5 Sundays occur and which months can have this rare event. Understand the probability behind it.
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