# What is the Probability that a Leap Year Has 53 Sundays and 53 Mondays? - Mathematics

What is the probability that a leap year has 53 Sundays and 53 Mondays?

#### Solution

We know that a leap year has 366 days (i.e. 7 $\times$ 52 + 2) = 52 weeks and 2 extra days.
The sample space for these two extra days is given by
S = {(Sunday, Monday), (Monday, Tuesday), (Tuesday, Wednesday), (Wednesday, Thursday), (Thursday, Friday), (Friday, Saturday), (Saturday, Sunday)}
There are 7 cases.
i.e. n(S) = 7
Let E be the event in which the leap year has 53 Sundays and 53 Mondays.
Then E = {(Sunday, Monday) }
i.e. n(E) = 1

$\therefore P\left( E \right) = \frac{n\left( E \right)}{n\left( S \right)} = \frac{1}{7}$
Hence, the probability in which a leap year has 53 Sundays and 53 Mondays is $\frac{1}{7} .$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 33 Probability
Exercise 33.3 | Q 6 | Page 46