Question

find the probability that an ordinary year has 53 sundays

Answer 1

The probability of a year being a leap year is 14and being non-leap is34

A leap year has 366 days or 52 weeks and 2 odd days. The two odd days can be {Sunday,Monday},{Monday,Tuesday},{Tuesday,Wednesday},{Wednesday,Thursday},{Thursday,Friday},{Friday,Saturday},{Saturday,Sunday}.

So there are 7 possibiliyies out of which 2 have a Sunday. So the probability of 53 Sundays in a leap year is 27.

A non-leap year has 365 days or 52 weeks and 1 odd day. The odd day can be Sunday,Monday, Tuesday,Wednesday,Thursday,Friday or Saturday.

So there are 7 possibilities out of which 1 is favorable. So the probability of 53 Sundays in non-leap year is 17.

So the probability of 53 Sundays in a year is 14×27+34×17

=228+328

=528

Note:The probability of a year being leap is normally taken to be 14 but more exactly it is 97400as out of century years only those divisible by 400 are leap. For example out of 2100,2200,2300,2400 only 2400 is leap

Answer 2

Hey !!

Here is your answer !!
____________________


❇ Ordinary year -- Non leap year
As we know that a non leap year has 365 days and that a year has 52 weeks
❇Hence there will be 52 Sundays for sure
As 52 × 7 = 364days
❇So 365-364 = 1 day extra
❇Hence this one day can be Sunday Monday Tuesday Wednesday Thursday Friday or Saturday
so total of 7 outcomes and 1 is favourable outcomes since we have to find only for Sunday
so
❇Probability will be ----- 1 / 7 ✔
______________


Hope its helpful for you !!
Have a great day !!☺