Question
What is the probability that a leap year has 53 Sundays ?
✓
Answer
A leap year has 366 days, which is equivalent to
52 weeks and 2 days.
52 weeks will have 52 Sundays.
The sample space for remaining two days can be
as follows:
$\therefore$ S= {Sunday-Monday, Monday-Tuesday, Tuesday -Wednesday, Wednesday-Thursday, Thursday-Friday, Friday-Saturday}
$\therefore n(S)=7$
Let A be the event of getting $53^{ rd }$ Sunday in remaining 2 days.
A = {Saturday-Sunday, Sunday-Monday}
$\therefore n(A)=2$
$P ( A )=\frac{n(A)}{n(S)}=\frac{2}{7}$
$\therefore$ The probability that a leap year has 53 Sundays is $\frac{2}{7}$.
52 weeks and 2 days.
52 weeks will have 52 Sundays.
The sample space for remaining two days can be
as follows:
$\therefore$ S= {Sunday-Monday, Monday-Tuesday, Tuesday -Wednesday, Wednesday-Thursday, Thursday-Friday, Friday-Saturday}
$\therefore n(S)=7$
Let A be the event of getting $53^{ rd }$ Sunday in remaining 2 days.
A = {Saturday-Sunday, Sunday-Monday}
$\therefore n(A)=2$
$P ( A )=\frac{n(A)}{n(S)}=\frac{2}{7}$
$\therefore$ The probability that a leap year has 53 Sundays is $\frac{2}{7}$.
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