perplexus.info :: Probability : Blue Moon

Blue Moon (Posted on 2007-06-07)

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
Great	Tatiana Espinoza	2024-06-13 12:02:22
Puzzle Answer	K Sengupta	2023-08-04 08:54:53
solution	Charlie	2007-06-07 16:56:31

Please log in:

Login:
Password:
Remember me:

Sign up! \| Forgot password

Search:

Search body:

Forums (1)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (6)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info