What is the probability that a leap year selected at random contains either 53 Thursday or 53 Friday

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JEE QuestionsThe Probability That A Leap Year Selected At Random Will Contain Either 53 Thursday Or 53 Friday Is

The probability that a leap year selected at random will contain either 53 Thursday or 53 Friday is

1) 3/7 2) 2/7 3) 5/7 4) 1/7

In a leap year, we have 366 days. It means, leap year contains 52 weeks and 2 days. The extra days will be anyone of the combinations:

{ Monday and Tuesday, Tuesday and Wednesday, Wednesday and Thursday, Thursday and Friday, Friday and Saturday, Saturday and Sunday, Sunday and Monday}

So we have 7 combinations.

Let X and Y be the event that the leap year contains either 53 Thursday or 53 Friday.

So, P(X) = 2/7, P(Y) = 2/7, P(X∩Y) = 1/7

Hence, the required probability = P(A∪B)=P(A)+P(B)−P(A∩B)

= (2/7) + (2/7) – (1/7)

= (4/7) – (1/7) = 3/7.

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What is the probability that a leap year, selected at random, will contain either 53 Thursdays or 53 fridays?

Answer (1 of 13): A leap year has 366 days, which comes out to 52 weeks and 2 days. That means that 2 of the days of the week will appear 53 times, while the other 5 days appear just 52 times each. For instance, a leap year that starts on a Thursday will have 52 complete weeks plus a Thursday and...

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Probability (statistics)

What is the probability that a leap year, selected at random, will contain either 53 Thursdays or 53 fridays?

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13 Answers

Manjunath Subramanya Iyer

, I am a retired bank officer teaching maths

Answered 4 years ago · Author has 6.3K answers and 6.4M answer views

Originally Answered: What is the probability that a leap year selected at random will contain either 53 Thursdays or 53 Fridays?

A leap year has 366 days. Now 364 is divisible by 7 and therefore there will be two excess week days Ina leap year. The two excess week days can be (Sunday, Monday), (Monday, Tuesday), (Tuesday, Wednesday), (Wednesday, Thursday), (Thursday, Friday), (Friday, Saturday), (Saturday, Sunday). So, the sample space S has 7 pairs of excess week days. i.e. n(S) = 7.

Now we want the desired event E to be 53 Thursdays or 53 Fridays. E consists of the pairs (Wednesday, Thursday), (Thursday, Friday), (Friday, Saturday). So, n(E) = 3.

Hence, the probability that a leap year selected at random will contain ei

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Kevin Jeffries

Answered 4 years ago

Originally Answered: What is the probability that a leap year selected at random will contain either 53 Thursday or 53 Friday?

A leap year has 366 days, which comes out to 52 weeks and 2 days. That means that 2 of the days of the week will appear 53 times, while the other 5 days appear just 52 times each. For instance, a leap year that starts on a Thursday will have 52 complete weeks plus a Thursday and a Friday left over at the end of the year, so Thursday and Friday will both appear 53 times each in that year. Similarly, a leap year that starts on Wednesday will have a 53rd Wednesday and Thursday, and a year that starts on Friday will have a 53rd Friday and Saturday.

The question of which leap years have 53 Thursdays

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Naresh Adapa

, works at SRM Institute of Science and Technology

Answered 3 years ago · Author has 74 answers and 139.9K answer views

3/7 366=52 week+2 days

that extra two days can be (su,m)(m,tu)(tu,w)(w,th)(th,f)(f,sa)(sa,su)

total 7 possiblties out of those 3 are favourable

if they ask for thursday and friday only one favourable,so probability=1/7

5.5K viewsView upvotes

Ankur Aggarwal

, IITJEE Maths Faculty at Allen Institute, Jaipur (2001-present)

Answered Mar 30, 2022 · Author has 457 answers and 94.4K answer views

Originally Answered: What is the probability that a leap year selected the rendom will contain either 53 Thursdays or Fridays?

In a leap year there are 366 days thus probability of getting 53 Thursday is =2/7 as remaining 2 can be Wednesday _ Thursday or Thursday _ Friday from seven total case.

Similarly probability of getting 53 Friday is= 2/7

Out of these cases Thursday _ Friday is common and probability of getting it =1/7

Thus required probability =2/7+2/7–1/7=3/7.

608 viewsView upvotes

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James Geschwindt

, Took 5 college math courses.

Answered 3 years ago · Author has 585 answers and 1.5M answer views

Originally Answered: What is the probability that a leap year selected at random will contain either 53 Thursdays or 53 Fridays?

A leap year contains 366 days. Therefore two consecutive days of the week will occur 53 times (the weekdays corresponding to the first two days of the year) and the remaining five consecutive days will occur 52 times.

For example if the first day of the leap year is a Monday, then Monday and Tuesday will occur 53 times and Wednesday, Thursday, Friday, Saturday, and Sunday will each occur 52 times.

So there are 7 possible leap years:

1. Leap year starts on a Monday, result: 53 Mondays and 53 Tues...

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The probability that a leap year selected at random will contain either 53 Thursday or 53 Friday is

3/7The probability that a leap year selected at random will contain either 53 Thursday or 53 Friday is

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The probability that a leap year selected at random will contain either 53 Thursday or 53 Friday is

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the questionnaire is the probability that a leap year selected at random will contain 53 Thursday of 53 Fridays where to find the probability for this in a leap year in a leap year how many days do we have you will have a 360 days 366 days so it is a leap year contains vitamin A will contain 52b leap year will contain 52 weeks and 2 test 52 weeks and Earth today at these two days these two days these are the extra today's and these two days will be a combination of any of today's weather there will be a combination of whether there will be a combination of Monday Tuesday Monday and Tuesday or whether there will be a method will be a combination of Tuesday and Wednesday Tuesday and Wednesday or they will be a combination of Wednesday and Thursday

there will be a combination of Thursday and Friday Thursday and Friday or they will be a combination of frightened Saturday Friday and Saturday or they will be a combination of Saturday and Sunday or else they will be a combination of Saturday and Sunday order will be a combination of Sunday and Monday Sunday and Monday so how many total number of possible outcomes that will have is 1234567 there are 7 number of combinations how many number of combinations do we have so we have a 7 combinations we will have a 7 combinations now what we have to find the probability that they reflected that they contain 53 Thursday and 53 Fridays to hear that here let x x and y v the event of leap year be the event of leap year will contain 53

53 53 53 Thursday and 53 Friday 53 Sajde aur 53 Fridays at the total number of probability that we will have is types of eggs will be equal to the number of days that will have its root 2 upon the number of combinations that we have a 7 similarly for P of we will have the number of days that is true and the number of Total to have that is 7 and hear the value of P and attractive to why will be equals to 1 upon 7 the value of P and the second to X intercept to find the probability to for finding the probability will be = true probability in the week was to create times of physical therapy of a union to we will equal to P of A+ of fee of b - of fee of a intersecting to be Manu Sobti of intersecting to be rescued the value of the value of P of

is 2.7 plus Sar value of fever that mystery of by that is also a 2.7 - 3 of 8 pattern to be your accent expecting to why that is one up on 7:00 overall the LCM that you will have is 7:00 over here and here there LCM will become 22044 - of one will become 4 - of one will become 3.3.7 is verified probability that the other contents that the leap year selected at random will contain 53 Thursday and 53

সংশ্লিষ্ট ভিডিও

644365660 2.2 K+ 3.2 K+ 3:38

The probability that a leap year selected at random will contain either 53 Thursday or 53 Friday is

647522015 5.8 K+ 7.1 K+

The probability that a leap year selected at random will contain either 53 Thursday or 53 Friday, is

464012836 100+ 2.1 K+ 1:43

The probability that a leap year selected at random will contain 53 Sundays or 53 Mondays is :

402313959 3.5 K+ 8.3 K+ 2:24

Find the probability that a non leap year selected at random will have 53 fridays.

402314076 800+ 9.3 K+ 4:30

Find the probability that a leap year selected at random will have 53 fridays.

7504732 6.2 K+ 9.8 K+ 1:38

What is the probability that a leap year will contain 53 Thursdays?

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