Question

We have the years from 2001, 2002, 2003,... to 2010. say, a year is chosen at random from the listed years. what is the probability that the chosen year has 53 mondays

Answer 1

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In 400 years (a Gregorian calendar cycle) there are 365×303+366×97=146097days which is 1460977=20871 weeks and so there are 20871 Mondays.

Since 20871=329×52+71×53, there are 71 years with 53 Mondays, and so the probability that a year has 53 Mondays is 71400=0.1775.

Similar calculations over a 400 year cycle can show that the 13th of a month is more likely to be a Friday than another other particular day