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.

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31-day months (January, March, May, July, August, October, December) will always have at least 4 Sundays. The probability of getting 5 Sundays is high. Check the monthly calendar: If the month starts on a Sunday, Monday, or Tuesday, it will contain 5 Sundays. With 7 possible start days, the probability is about 3/7 or roughly 43%.

FAQs & Answers

  1. Which months have 31 days and can have 5 Sundays? January, March, May, July, August, October, and December are the months with 31 days that can contain 5 Sundays.
  2. What determines if a 31-day month will have 5 Sundays? The day of the week the month starts on affects this. If the month starts on Sunday, Monday, or Tuesday, it will likely have 5 Sundays.
  3. What is the probability of a 31-day month having 5 Sundays? Since there are 7 possible start days in a week, and starting on Sunday, Monday, or Tuesday results in 5 Sundays, the probability is about 3/7 or approximately 43%.
  4. Do all months with 31 days always have 5 Sundays? No. Although every 31-day month has at least 4 Sundays, only those starting on Sunday, Monday, or Tuesday have 5 Sundays.