Probability Involving Calender

Calender: 

It is a chart showing the days, weeks, and months of a particular year, or giving particular seasonal information. In a year there are 365 days 6 hours

The 365 days are divided into 12 months. The months January, March, May, July, August, October and December have 31 days, whereas April, June, September and November have 30 days. The month of February has 28 days in a normal year and 29 days in a leap year. The Leap Year is after every four years. As a Year has 365 days and 6 hours. The 6 hours of these four year are collected to make 24 hours hence one day extra. This extra day is added to the month of February.

Each year has 52 weeks and one day. Each day of the week occurs 52 times, except the day the year started that day will occur 53 times in a year because a year has 52 weeks and 1 day extra. This one day will lie on the same day the year started. For example, if a year started on Monday then the 52 weeks will end on Sunday. And the extra day will fall on Monday. So only the day of the week it started will occur 53 times and all other will occur 52 times. In case of a leap year there are two days extra, so if the year started on Monday then it will have 53 Mondays and 53 Tuesdays. This information is used while solving question on calendar

Illustration:  What is the probability that a non-leap year will have 53 Sundays?

Solution:  A non-leap year contains 365 days, so that it has 52 complete weeks and one extra day. This extra day can be any one of the following 7 possible days.

(i) Sunday  (ii) Monday  (iii) Tuesday  (iv) Wednesday  (v) Thursday  (vi) Friday  (vii) Saturday

Out of these seven possibilities just one, the first one, is favourable to the occurence of the event 53 Sundays

So the number of favourable cases = 1

Total Outcomes: 7

Illustration:  What is the probability that a leap year will have 53 Sundays?

Solution:  A leap year contains 366 days, so that it has 52 complete weeks and two extra days. These two extra days can be any one of the following 7 possible combinations.

(i) Sunday, Monday                  (ii) Monday, Tuesday                      (iii) Tuesday, Wednesday                                    (iv) Wednesday, Thursday

(v) Thursday, Friday                 (vi) Friday, Saturday                       (vii) Saturday, Sunday

Out of these 7 possible combinations, only the (i) and (ii) are favourable to the occurence of the event 53 Sundays.

So the number of favourable cases = 2

Total Outcomes: 7