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Blue Moon (Posted on 2007-06-07) Difficulty: 3 of 5
The most common current definition of a blue moon is the second full moon of a calendar month.

Given that the full moon occurs every 29.5 days what is the long term probability that when a blue moon occurs it is in a specific month? Use the regular (every 4th year) leap year formula for February.

Consider a world/calendar with a lunar cycle of exactly 29 days and whose months are randomly assigned 30 or 31 days (with equal probability and no yearly repetition.) What is the long term probability that a blue moon falls on a 30 day month?

  Submitted by Jer    
Rating: 3.0000 (1 votes)
Solution: (Hide)
31 day months are 3 times as likely to have a blue moon than a 30 day month. This is because (31-29.5) is three times (30-29.5). February can never have a blue moon.

So call the probability of each of the 30 day months p and for the 31 day months 3p.

There are four 30 day months and seven 31 day months.

4(p) + 7(3p) = 1 25p = 1 p=1/25

So the probability for any given 30 day month is 1/25 and for a 31 day month it is 3/25

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Puzzle Answer K Sengupta2023-08-04 08:54:53
SolutionsolutionCharlie2007-06-07 16:56:31
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