# Probabilty Problem

1. Aug 8, 2007

### suganya

Hi,

What is the chance that an ordinary year selected at random contains53 Sundays.

How to work it.

Regards,
Suganya

EasyCalculation
ToFocus

2. Aug 8, 2007

### daveb

If by ordinary year you mean non-leap year, then under what circumstances will a year have 53 Sundays?

3. Aug 8, 2007

### CRGreathouse

What if the year starts on a Sunday? What if it starts on a Monday? How often does it start on each day in a given calendar (just assume 1/7 for a first estimate)?

4. Sep 7, 2007

### Esd

Well, a general year here is 365 days. Dividing it into weeks (by 7) would leave a remainder of 1. Where there would be 52 weeks and 1 day. We can assume that those 52 weeks would mean 52 Sundays (now working with an imaginary 364 day-year, just because it doesn't leave the remainder of 1). To have the 53 Sundays is when the remainder of 1 comes in. Suppose you had our imaginary year of 364 days and let's say it began on a Monday, thus neatly ending on a Sunday. Should we add the remainder of 1 at the end, there will be an extra Monday (Monday now = 53). To be more relevant to your case, it would be easier to start this with a 364 day-year that ended with a Saturday, and thus began with a Sunday. (Imagine moving a 364 day interval left, which is set on a continuous background of Monday-Sunday cycles). So now we add the remainder, to get 365 days, and we have a Sunday at the end (Sunday now = 53). Should we move this year left, it will be a year that starts with a Saturday and ends with a Saturday (original Sunday still contained, but the one at the end is cut off, now Sunday = 52). We could have started this by adding that remainder to the beginning of the year, and it wouldn't have made a difference. Point is, a 365 day year begins with the same day it ends. That last day makes a day of the week = 53, compared to the other 6/7 days which are at 52. Thus the question can be reduced to - "What are the chances that a year starts with a Sunday?".(assuming you mean a non-leap year). There are 7 choices, hence 1/7. Hope I'm right, as I'm half asleep.