# if a leap year is chosen at random, what is the probability that there are exactly 52 sundays in it?

### Mohammed

Guys, does anyone know the answer?

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## The probability that a leap year will have only 52 Sunday, is

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JEE QuestionsThe Probability That A Leap Year Will Have Only 52 Sunday Is

## The probability that a leap year will have only 52 Sunday, is 1) 4/7 2) 5/7 3) 6/7 4) 1/7

**Solution:**Option (2) 5/7

In a leap year, we have 366 days. So, we have 52 weeks and 2 days.

So, the 2 days will the combination of {(Sunday, Monday), (Monday, Tuesday), (Tuesday, Wednesday), (Wednesday, Thursday), (Thursday, Friday), (Friday, Saturday), (Saturday, Sunday)}

Out of these, 7 pairs of combinations, only 2 pairs have Sunday, and the other 5 pairs do not have Sundays.

Therefore, the probability that a leap year will have only 52 Sundays is 5/7.

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## The probability that a leap year will have only 52 Sundays is

Click here👆to get an answer to your question ✍️ The probability that a leap year will have only 52 Sundays is

Question

## The probability that a leap year will have only 52 Sundays is

**A**

7 4

**B**

7 5

**C**

7 6

**D**

7 1 Easy Open in App Solution Verified by Toppr

Correct option is B)

No. of days in a leap =366( 7 366 =52.28)

So, there will be 52 weeks and 2 days

So, every leap year has 52 Sundays

Now, the probability depends on remaining 2 days

The possible pairing of days are

Sunday-Monday Monday-Tuesday Tuesday-Wednesday Wednesday-Thursday Thursday-Friday Friday-Saturday Saturday-Sunday

There are total 7 pairs and out of 7 pairs, only 2 pairs have Sunday. The remaining 5 pairs does not include Sunday

Thus, the probability of not getting Sunday in the last 2 days is

7 5

Therefore, the probability of only 52 Sundays in a Leap year is

7 5 . Video Explanation

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## Find the probability of getting exactly 52 Sundays in a leap year?

Answer (1 of 10): EArlier I also thought , it should be 1 but more understanding and practising the questions on probability , my concept became clearer. A leap year has 366 days = 52 *7 + 2 . So, there are 52 weeks i.e. 52 sundays but the two extra days changes the game. Now , we have to focu...

Find the probability of getting exactly 52 Sundays in a leap year?

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Sort Shubham Acharya

Studied at Indian Institute of Science, Bangalore (IISc) (Graduated 2020)Author has 60 answers and 817.8K answer views6y

The question is asking the probability of getting "exactly" 52 Sundays and not at least 52 Sundays.

There are 52 weeks in a year, so there will be 52 Sundays, no two questions about it. However,

52∗7=364 52∗7=364

so that still leaves a day for a normal year, and two days for a leap year.

Now, let us look at the combinations of the two days possible.

(Sunday, Monday), (Monday, Tuesday), (Tuesday, Wednesday), (Wednesday, Thursday), (Thursday, Friday), (Friday, Saturday), (Saturday, Sunday)

Now, to get exactly 52 Sundays, none of the last two days should be a Sunday. As you can see from the combinations liste

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Sanjay Mundhra

love to play with mathematics questions !Author has 58 answers and 415.2K answer views6y

EArlier I also thought , it should be 1 but more understanding and practising the questions on probability , my concept became clearer.

A leap year has 366 days = 52 *7 + 2 .

So, there are 52 weeks i.e. 52 sundays but the two extra days changes the game.

Now , we have to focus on these 2 days .

The extra 2 days is the main concept to understand = (sunday, monday) , (monday-tuesday) , (tuesday-wednesday) ,(wednesday-thursday) ,(thursday-friday) , (firday-saturday), (saturday-sunday)

If any of the t...

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Sayak Chowdhury

Knows Old EnglishAuthor has 197 answers and 799.8K answer views5y

In a leap year there are 52 weeks, and two remaining days.

Those two days are consecutive, so there can 7 equally likely pairs.

Among the 7 pairs, (Saturday, Sunday) and (Sunday, Monday) pair will result in 53 Sundays.

So unfavourable pairs are these 2, rest (7–2=5) pairs are favourable.

So the probability = 5/7

Sahil Prajapati

Master of Engineering in Electronics & Communication, Parul Institute of Engineering and Technology (Graduated 2015)Author has 752 answers and 2.9M answer views4y

Leap Year has 366 days

52*7=364 days + 2 days extra

The probability of having 52 Sundays in a leap year is the remaining two days can be any of this formation: Sunday-Monday, Monday-Tuesday, Tuesday-Wednesday, Wednesday-Thursday, Thursday-Friday, Friday-Saturday, Saturday-Sunday.

However, to get 52 Sundays in a leap year, none of the remaining two days must be a Sunday. SO it’s probability by simple rule is 2/7

So, by the rule of probability it will come 1–2/7

Answer is- 5/7 Related questions

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Uffe Rasmussen

Freelance IT-consultant4y

You run through a leap year cycle, i.e. 400 consecutive years. In these there are 100 - 4 + 1 = 97 leap years of 366 days = 52 weeks and two days.

Is January 1st a Sunday, December 30th will be too. The same happens for January 2nd and December 31st. These two scenarios, and only these, are equal to that the number of Sundays in the leap year is 53.

It happens in 28 of the 97 leap years in the cycle. So the probability you are looking for is (97–28)/97 = 69/97.

If you want to ask the same for one of six others day of the week, the number 28 still can be used, except for Tuesdays and Thursdays, wh

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Tim Zukas

Author has 5.5K answers and 1.8M answer views4y

Everyone except Uffe Rasmussen is assuming that exactly one out of seven leap years starts on a Sunday, one out of seven starts on a Monday, and so on. He’s not taking that for granted.

I’m too lazy to confirm it, but I suspect his calculation is correct, assuming no future improvements to the Gregorian calendar.

(On the other hand, if we’re discussing a Julian-calendar year, then 5/7 is the correct probability after all. The Julian calendar repeats after 28 years, so it’s easier.)

Tarun Malviya

Former Derivatives TraderAuthor has 89 answers and 210.3K answer views7y

Originally Answered: Find the probability of getting 52 Sundays in a leap year?

I think it means exactly 52 Sundays

Now if first day is Sunday in a 365 days year there will be 53 Sundays and in a leap year if first day is either Sunday or Saturday then there will be 53 Sundays, so in normal year probability of Sunday is 6/7 and in leap year is 5/7 if question asks for exactly 52 Sundays and 1 for at least 52 sundays

Guys, does anyone know the answer?