Probability that a Year with 53 Sundays is a Leap Year?

[sheldonrocks97]

Homework Statement

A year has 53 Sundays. What is the conditional probability that it is a leap year.

Homework Equations

None that I can think of.

The Attempt at a Solution

I tried by knowing that a leap year has 366 days. Next we can note that the remaining 2 days could be sunday and monday, monday and tuesday, ... and saturday and sunday. Sunday appears 2 out of 7 times, so the answer I got was 2/7. Is that correct or did I do something wrong?

 

[RUber]

You forgot the conditional part.
If A = 53 Sundays and B= Leap Year, you found p(A|B). You want p(B|A).
You still need to know the probability of 53 Sundays on a non-leap year.

 

[haruspex]

To answer this you need to use knowledge of how often leap years occur. The questioner probably expects you to use 1/4, but strictly speaking it's (1/4-1/100+1/400).