Find the probability of getting 53 saturdays in leap year.

M4maths Previous Puzzles

12 Mar 2013 probability

Find the probability of getting 53 saturdays in leap year.

OPtion

1) 7/52
2) 7/53
3) 53/365
4) 2/7
5) 7/365
6) 2/9
7) 2/53
8) 4/7
9) 1/7
10) None of these

Solution

In a leap year, there are 366 days. Out of these 364 days make 52 weeks and hence 52 saturday. Remaining 2 days can be: Sun-Mon, Tue-Wed, Wed-Thu, Fri-Sat, Sat-Sun.
Total number of possible outcomes = 7
No of saturday outcomes = 2 (Fri-Sat, Sat-Sun)
Then probability of 53 saturdays = 2/7

Correct Option: 4 Best Solution (18)

AVINASH KUMAR   11 years AGO

Leap year consist of 366 days.
On that we have, 52 weeks and 2 days.
Extra 2 days may be

Sun,Mon
Mon,Tue
Tue,Wed
Wed,Thu
Thu,Fri
Fri,Sat
Sat,Sun

We have 7 options.
Among that we have to choose only 2 options which has saturdays . (i.e, [Fri,Sat] or [Sat Sun]

So that, the answer is 2/7 for having 53 Sundays.

Like? Yes (14) | No (5)  

Kalpesh   11 years AGO

In a Leap Year, there are 366 Days.
366 Days = 52 Weeks and 2 Days
Thus, a Leap Year has always 52 Saturdays.

The Remaining 2 Days can be :

(i) Sunday & Monday ; (ii) Mon & Tue ; (iii) Tue & Wed ; (iv) Wed & Thu ; (v) Thu & Fri ; (vi) Fri & Sat ; (vii) Sat & Sun.

Clearly there are 7 Elementary events associated.
Let A be the event that a Leap Year has 53 Saturdays.
Clearly, the event A will happen if the last two days of the leap year are either Sun & Mon or Sat & Sun.

Favourable Outcomes = 2

Required Probability = 2/7.

Like? Yes (4) | No (2)  

Rats   11 years AGO

In a leap year, there are
366days = 52weeks and 2days
A leap year always has 52sundays
For remaining 2 days, there are 7 possible outcomes
(1.Sun&Mon 2.Mon&Tue 3.Tue&Wed 4.Wed&Thu 5.Thu&Fri 6.Fri&Sat 7.Sat&Sun)
From these there are 2 favourable outcomes i.e.
1.Sun&Mon 2.Sat&Sun
So probability of getting 53 sundays=2/7

Like? Yes (5) | No (4)  

Balakumaran N.A   11 years AGO

In a Leap Year, there are 366 Days.
366 Days = 52 Weeks and 2 Days
Thus, a Leap Year has always 52 Sat.
The Remaining 2 Days can be :
(i) Sunday & Monday ; (ii) Mon & Tue ; (iii) Tue & Wed ; (iv) Wed & Thu ; (v) Thu & Fri ; (vi) Fri & Sat ; (vii) Sat & Sun.
Clearly there are 7 Elementary events associated.
Let A be the event that a Leap Year has 53 Saturdays.
Clearly, the event A will happen if the last two days of the leap year are either Fri & Sat or Sat & Sun.
Favourable Outcomes = 2
Required Probability = 2/7.

Like? Yes (4) | No (4)  

D.Jagruthi   11 years AGO

in a leap year there are 366 days=52 weeks and 2 days
The Remaining 2 Days can be :
(i) Sunday & Monday ; (ii) Mon & Tue ; (iii) Tue & Wed ; (iv) Wed & Thu ; (v) Thu & Fri ; (vi) Fri & Sat ; (vii) Sat & Sun.
Clearly there are 7 Elementary events associated.
Let A be the event that a Leap Year has 53 Saturdays.
Clearly, the event A will happen if the last two days of the leap year are either Fri & Sat or Sat & Sun.
Favourable Outcomes = 2
Required Probability = 2/7.

Like? Yes (2) | No (2)  

jitendra singh   11 years AGO

2/7

Like? Yes (3) | No (3)  

krishnapriya   11 years AGO

366 days=52 weeks & 2 days
Thus, a leap year has always 52 saturdays
Let A be the event that a leap year has 53 saturdays
Favorable outcomes=2
Required Probability=2/7

Like? Yes (1) | No (1)  

Dhivya   11 years AGO

in leap 366 days
52 weeks so 52 saturdays
remaining 2 days
it may be
sun-mon
mon-tue
tue-wed
wed-thurs
thurs-fri
fri -sat
sat-sun
so
its 2/7

Like? Yes (4) | No (4)  

RAHUL RAJ   11 years AGO

IN a Leap year there are 366 days
366/7=52 weeks and 2 days.
In extra two days probability of getting a saturdays is 2/7

Like? Yes (2) | No (3)  

Devendra Marghade   11 years AGO

In a leap year of 366 days
If 1 st Jan is Saturday,then 1+(52*7)=365th day &
If 2 nd Jan is Saturday,then 1+(52*7)=366th day will be Saturday
So probability=2/7

Like? Yes (1) | No (2)  

ArunKumar   11 years AGO

Leap Year has 53 Saturdays.
Clearly, the event A will happen if the last two days of the leap year are either Sun & Mon or Sat & Sun.

Favourable Outcomes = 2

Required Probability = 2/7.

Like? Yes (3) | No (4)  

sumit jindal   11 years AGO

Leap Year=366 days= 52 weeks + 2 days
so probability for saturday = 1/7+ 1/7 =2/7

Like? Yes (2) | No (3)  

raghunath reddy   11 years AGO

366 days = 52 weeks + 2 days, the two day can be mon, tue
tue, wed
wed, thur
thur, fri
fri, sat
sat, sun
sun, mon
So, 2 ways out of 7 i.2 2/7

Like? Yes (2) | No (3)  

Abhilash Mishra   11 years AGO

as we know,
in leap year we have 2 extra days after 52 weeks.
thus, the probability of coming of any day in the extra days(53rd time in a year) is 2/7.
as 2 days can occur out of 7 days.

Like? Yes (2) | No (3)  

Vinay Sipani    11 years AGO

leap year => 366 days => 52 weeks + 2days
=> 52 saturdays + 2 days

Among 2 consecutive days,
probability of getting one saturday = 2/7

Like? Yes (1) | No (2)  

Sanjeewani Indurkar   11 years AGO

complete weeks in leap year is 366/7=52(quotient) and remainder is 2 (Extra days)..
so from this extra two days, first day can be saturday or the second day can be saturday. Hence the probablity will be 1/7+1/7=2/7

Like? Yes (2) | No (4)  

Dr.Dipin Singh   11 years AGO

In a leap year, there are 366 days where 2 days of week are appearing 53 times.
If 1st january is Saturday or Friday out of 7 days of week, then we get 53 saturdays in a leap year.
so probability of getting 53 saturdays in leap year = 2/7

Like? Yes (3) | No (5)  

dharmendra   11 years AGO

case1:if year start with friday then total no of saturday is 53
case 2:if year start with saturday then also total no saturday is53
this is true for only two cases out of possible seven cases so
probability=2/7

Like? Yes (2) | No (4)