Find the probability that a leap year will have 53 friday or 53 saryday?

Question

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Answer 1

A leap year has 366 days.  Since there are 7 days in each week, that is 52 weeks and 2 days.

 

Now, a leap year may start on any of 7 days.  If we want to find out when a leap year has either 53 Fridays or 53 Saturdays, that means it must start on Th, F, or Sa.  Here is a table:

      Start on     End on       Number of Fridays          Number of Saturdays      Success?

         Su              M                     52                                     52                      n

         M               Tu                    52                                     52                      n

         Tu              W                    52                                     52                      n

         W               Th                   52                                     52                      n

         Th              F                     53                                     52                    Y

         F                Sa                   53                                     53                    Y

         Sa              Su                   52                                     53                    Y

 

Definition of probability = (number of successful outcomes) / (number of possible outcomes)

 

P (a leap year has 53 F or 53 Sa) = 3/7

Answer 2

This is a rather complicated question.

 

Each year has 365 or 366 days. The rule for whether there is a leap day is a complicated rule;if the year is a multiple of four, LEAP year, except if a multipe of 100, NOT A LEAP year, except if a multiple of 400, it is a leap year anyway, unless it's  multiple of 1600, in which case it's NOT A LEAP YEAR.  This is an empirical rule that attempts to keep calendars accurate, based on the length of a sidereal year. For fun, you might also look up the concept LEAP SECOND which has been applied a couple of times during my lifetime.

 

Now, 365 days contains 52 weeks plus one day; that means some year will have 53 instances of a particular day--that will depend upon what day the year began with; that beginning day will be the one (i.e. its name) that occurs an extra time. And a leap year will have 53 instances of the first two days of that particular year.

 

When it comes to probability of leap year, what is the Sample Space--that's another problem.