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

  1. Jan 28, 2015 #1

    sheldonrocks97

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    1. The problem statement, all variables and given/known data
    A year has 53 Sundays. What is the conditional probability that it is a leap year.

    2. Relevant equations
    None that I can think of.

    3. 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?
     
  2. jcsd
  3. Jan 29, 2015 #2

    RUber

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    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.
     
  4. Jan 29, 2015 #3

    haruspex

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    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).
     
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