# What is the Probability that a Leap Year Will Have 53 Fridays Or 53 Saturdays? - Mathematics

What is the probability that a leap year will have 53 Fridays or 53 Saturdays?

#### 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 are as follows:
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 that a leap year has 53 Fridays or 53 Saturdays.
Then E = { (Thursday, Friday), (Friday, Saturday), (Saturday, Sunday)}
i.e. n(E) = 3

$\therefore P\left( E \right) = \frac{n\left( E \right)}{n\left( S \right)} = \frac{3}{7}$

Hence, the probability that a leap year has 53 Fridays or 53 Saturdays is $\frac{3}{7} .$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 33 Probability
Q 4 | Page 71