What is the probability that an ordinary year has 53 Sundays?

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There are 2 types of years: leap and normal. Leap years have 366 days and normal years have 365 days.

I also know that leap years occur once in 4 years. However, not all century years (e.g. 1900) are leap. A century year is leap if it is divisible by 400.

How do I compute this probability?


Step 1: Understand the given information in the question.

Step 2 : Recall the probability definition.

[Note: Probability of an event happening = Number of ways it can happen / Total number of outcomes.]

Step 3: Calculate the number of ways it can happen

In an ordinary year we have 365 days = 52 weeks + 1 day

So, we have 52 weeks means we have 52 Sundays in every week.

But, we need 53  Sundays in a year for that remaining one day also must be Sunday,

Number of ways it can happen = 1

Step 3: Calculate the Total number of outcomes.

In a week we have 7 days (Sun, Mon, Tue, Wed, Thu, Fri, Saturday.)

So Total number of outcomes. = 7

Step 4: Substitute the values in the formula.

Probability that an ordinary year has 53 Sundays = 1/7.

Sangeetha Pulapaka
Neatly put!
Mahesh Godavarti
How about taking into account the possibility of a leap year?