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 $\frac{2}{7}$.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
How many numbers are there between $101$ and $999$, which are divisible by both $2$ and $5$?
→In the following figure, O is the centre of a circular arc and AOB is a straight line.
Find the perimeter and the area of the shaded region correct to one decimal place. $\big(\text{Take }\pi=3.142\big)$
→Find the perimeter and the area of the shaded region correct to one decimal place. $\big(\text{Take }\pi=3.142\big)$
If $ad \neq bc$ then prove that the equation $(a^2 + b^2)x^2 + 2(ac + bd)x + (c^2 + d^2) = 0$ has no real roots.
→A train travels 360 km with uniform speed.The speed of the train is increased by 5 km/hr, it takes 48 minutes less to cover the same distance. Find the initial speed of the train.
Following is the cumulative frequency distribution of employees in a certain office according to age.
Find the median age of employee.
| Age | less than 20 | less than 25 | less than 30 | less than 35 | less than 40 | less than 45 | less than 50 | less than 55 | less than 60 |
| Cumulative frequency | 0 | 2 | 8 | 22 | 51 | 88 | 105 | 108 | 110 |
In figure 3.51 , chord $\mathrm{LM} \cong$ chord $\mathrm{LN}$ $\angle \mathrm{L}=35^{\circ}$ find
(i) $m(\operatorname{arc} \mathrm{MN})$
(ii) $m(\operatorname{arc} \mathrm{LN})$
→(i) $m(\operatorname{arc} \mathrm{MN})$
(ii) $m(\operatorname{arc} \mathrm{LN})$
The sum of two number $a$ and $b$ is $15$, and the sum of their reciprocals $\frac{1}{\text{a}}$ and $\frac{1}{\text{b}}$ is $\frac{3}{10}.$ Find the numbers a and b.
→The following pie diagram represents the number of valid votes obtained by four students who contested for school captain. The total of valid votes polled was 720. Answer the following questions.
(i) Who has won the election?
(ii) What is the minimum no. of votes? Who got it?
(iii) By how many votes did the winner defeat the nearest contestant?
(i) Who has won the election?
(ii) What is the minimum no. of votes? Who got it?
(iii) By how many votes did the winner defeat the nearest contestant?
The following table shows the marks of 180 students in Mathematics. Find the value of '$x$' and draw histogram.
Find the value of ‘$x$’ and draw histogram.
→| Marks | No. of Students |
| 0 - 10 | 25 |
| 10 - 20 | $x$ |
| 20 - 30 | 30 |
| 30 - 40 | $2x$ |
| 40 - 50 | 65 |
A ladder is placed in such a way that its foot is at a distance of 15m from a wall and its top reaches a window 20m above the ground. Find the length of the ladder.