Question

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

Answer 1

Step 1: Find the sample space of the given leap year

We have $366$ days in a leap year

There are $52$weeks and $2$ days

However, two days can be

$S=(Sun,Mon),(Mon,Tue),(Tue,Wed),(Wed,Thru),(Thru,Fri),(Fri,Sat),(Sat,Sun)$

$n\left(S\right)=7$

Step 2: Find the probability that a leap year has $53$ Sundays and$53$ Mondays

Now desirable is (Sun, Mon) because that will make $53$ Sunday and$53$Monday, that is,

$n\left(E\right)=1$

Therefore, $P=\frac{n\left(E\right)}{n\left(S\right)}=\frac{1}{7}$

Final answer:

The probability that a leap year has $53$ Sundays and$53$ Mondays is $\frac{1}{7}$