Monday, December 29, 2014

Are the 7 long weekends in 2015 truly a "bumper crop"?

A long weekend occurs when a public holiday falls on a Monday, Friday, or Sunday (when a public holiday falls on a Sunday, Monday is also a holiday). This makes three out of seven days, which means that the odds of a long weekend are pretty high, at slightly under half.

For 2015, we have long weekends on 7 out of the 11 public holidays, a "bumper crop", according to the Straits Times. Is this truly a long weekend bonanza, or something closer to the theoretical average?

For most public holidays, the odds of the holiday falling on Monday, Friday, or Sunday are 3/7 = 43%. However, not all holidays are the same. Firstly, there are two consecutive holidays during Chinese New Year. Because of this, the probability of getting a long weekend over Chinese New Year is higher than that for other public holidays. Secondly, Good Friday guarantees you at least one long weekend a year.

Hence, I used some combinatorics to account for different holiday permutations, and calculated the probability of getting varying numbers of long weekends a year. The results are presented in the chart below.

Source: author's calculations
As shown above, the probability of having 5 long weekends is slightly above 25%. In most years, 69% to be exact, we would expect 4 - 6 long weekends. Also, the expected number of long weekends each year is 5.1.

There are 7 long weekends in 2015. The odds of this happening is not high, at 12.4% only (or once every 8 years), so it truly is a bumper crop of long weekends.

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