Understanding the Calendar
An ordinary year consists of 365 days. This can be calculated as 52 weeks and 1 additional day.
Distribution of Days in a Week
- Each week has 7 days: Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, and Saturday.
- In 52 weeks, there are 52 occurrences of each day.
- The extra day determines if a specific day, like Monday, appears 53 times.
Extra Day Scenarios
- The extra day can be any of the 7 days of the week.
- If the extra day is a Monday, then that year will have 53 Mondays.
- The possible scenarios for extra days are:
- Year starts on Sunday: Extra day is Sunday.
- Year starts on Monday: Extra day is Monday.
- Year starts on Tuesday: Extra day is Tuesday.
- Year starts on Wednesday: Extra day is Wednesday.
- Year starts on Thursday: Extra day is Thursday.
- Year starts on Friday: Extra day is Friday.
- Year starts on Saturday: Extra day is Saturday.
Calculating the Probability
- There are 7 possible days for the extra day.
- Only 1 of these scenarios (when the year starts on a Monday) results in 53 Mondays.
Final Probability
- Thus, the probability that an ordinary year has 53 Mondays is:
- Number of favorable outcomes (1) / Total outcomes (7) = 1/7.
In conclusion, the probability that an ordinary year has 53 Mondays is approximately 14.29%.