From which year should I start counting leap years and where do I stop counting? I tried from 4AD to 2004. A leap year has 53 tuesdays only if starts on Mon or Tue. Accordingly, it gives me 137/500. Ans is 2/7. Wondering where am I going wrong?
2007-02-01 14:59:22 · 7 answers · asked by Mau 3 in Science & Mathematics ➔ Mathematics
The leap year arose from the creation of the Gregorian calendar in 1582. Thus, no year before 1584 could have been a leap year. Also, have you considered that in years ending 00, (1700, 1800, and 1900) were not leap years. Only years ending in 00 that are evenly divisible by 400 have the extra day (1600 and 2000). Thus, only 103 leap years have occurred, and these only in the countries which adopted the Gregorian calendar at it's onset (Catholic countries, Spain, Italy, Portugal).
Interestingly enough the First Leap year began on a Sunday. However, 3 leap years are lost (1700, 1800, 1900) which began on Monday, Friday, and Tuesday respectively. Thus, 28 of 103 leap years began on Monday or Tuesday; the answer is 0.27 (2/7 is 0.29).
Britain, hence the US adopted the Gregorian calendar in September 1752, the first leap year would have been 1756 (Monday). Since then there have been 63 leap years, 17 starting on either Monday or Tuesday 17/63 rounds to 0.27.
2007-02-01 15:38:38 · answer #1 · answered by Jimmy J 3 · 0⤊ 0⤋
First of all the number of leap years do not apply:
Since a leap year has 53 tuesdays only when it starts on Mon or Tues, then that is 2 days of the week out of 7. Thus 2/7
2007-02-01 23:04:06 · answer #2 · answered by AibohphobiA 4 · 1⤊ 0⤋
I get 27/97. The 500 leap years in your study had a bias.
Leaps years cycle around on a 400-year cycle, with 97 leap years in the cycle. There are exactly 20,871 weeks in the cycle.
Counting the days of the week for 1 Jan:
Sat 13
Sun 15
Mon 13
Tues 14
Wed 14
Thurs 13
Fri 15
It seems to me, that the book answer just assumed that the leap years would start on any day of the week, with equal probability.
2007-02-01 23:25:58 · answer #3 · answered by morningfoxnorth 6 · 0⤊ 0⤋
Based on the phrasing, it's obvious that the simple way was what was meant. Hence 2/7, as previously pointed out.
The probability of an event is NOT necessarily equal to the fraction of times it has occurred in a given sample. There's a strong connection between the two concepts, but they're not the same thing.
2007-02-02 00:11:28 · answer #4 · answered by Curt Monash 7 · 1⤊ 0⤋
it will be 2/7
2007-02-02 04:21:39 · answer #5 · answered by Bishnoi 2 · 1⤊ 0⤋
its simple we have 52 weeks + 2days =366 days
52*7=364
and now we have 2 days left......and to get 53 tuesdays the possible combinations are (monday, Tuesday) and (tuesday and wednesday)....so thera are 2 possible outcomes to satisfy the condition....so ans is 2/7
2007-02-01 23:15:38 · answer #6 · answered by funindra2003 2 · 2⤊ 0⤋
Ans is 2/21
2007-02-02 02:15:24 · answer #7 · answered by mohan p 1 · 0⤊ 1⤋