What is the probability that an ordinary year has 53 Sundays?

What is the probability that a leap year has 53 Tuesdays and 53 Mondays?

The probability of an ordinary year having 53 Sundays can be understood by looking at how days are distributed throughout the year. An ordinary year has 365 days, which equals 52 weeks and 1 extra day. This means there are 52 Sundays, and the extra day can be any day of the week. Therefore, there is a chance that this extra day is a Sunday.

Calculating the Probability for Ordinary Years

Since there are 7 days in a week, the probability of the extra day being a Sunday is:

• Number of favorable outcomes (Sunday) = 1
• Total possible outcomes (days of the week) = 7

The probability is:

P(53 Sundays in an ordinary year) = 1/7

Examining Leap Years

A leap year consists of 366 days, which translates to 52 weeks and 2 extra days. This means there are 52 of each day of the week, plus the possibility of having two additional days.

Probability for Leap Years

To find the probability of having 53 Tuesdays or 53 Mondays in a leap year, we need to consider the combinations of the two extra days:

• Extra days could be Sunday and Monday
• Extra days could be Monday and Tuesday
• Extra days could be Tuesday and Wednesday
• Extra days could be Wednesday and Thursday
• Extra days could be Thursday and Friday
• Extra days could be Friday and Saturday
• Extra days could be Saturday and Sunday

In this case, the extra days can include both a Monday and a Tuesday, which means:

P(53 Tuesdays or 53 Mondays in a leap year) = 2/7

Summary

In summary, the probability of an ordinary year having 53 Sundays is 1/7, while the probability of a leap year having 53 Tuesdays or 53 Mondays is 2/7.