Probability PGEE

Question

What is the chance that a leap year selected at random will contain 52 Sundays?

  a. 1

  b. 3/7

  c. 1/7

  d. 2/7

 

 

Answer 1

The question asks for "contain 52 Sundays" which means at least 52 Sunday. Any year whether leap or not will contain $\frac{365}{7} = 52$ Sundays. So, our answer is $$1.$$

Now, suppose the question is exactly 52 Sundays- meaning 53 Sundays is not favorable:

A leap year has 366 days. 

So, no. of complete weeks = 366/7 = 52. 

No. of remaining days = 366 mod 7 = 2.

So, we have 52 Sundays for sure and have 2 extra days. As per question we dont want the 2 of them to be Sundays. We have 7 choices for the 2 days

SM, MT, TW, WT, TF, FS, SS

All of these are equally likely (random choice of leap year) and 5 among these are favorable. So, our required probability will be 

$$\frac{5}{7}.$$

A catch for my explanation:
http://math.stackexchange.com/questions/652803/what-is-the-probability-that-a-leap-year-selected-at-random-will-contain-53-tues

Comments

No sir for a non leap year it should be 1/7 . SInce in non leap year it has 365 days =52*7(52 sundays ) + 1 ,

now this one day can be either mom tues wed and so on .

so prob of getting 53 sunday is 1/7 in a non leap year

---

but I told for 52 :)

---

ha then its fine sorry :) sorry sorry :(

Answer 2

A leap year has 52 weeks + 2 ordinary days

those 2 ordinary days can be SM,MT,TW,WTh,ThF,FS,SS

Removing sunday option from the above 
We get required probablity as
5/7

 

Comments

not precise. For subjective exam you might get even 90% mark for this but for objective it will be 0- we have to give what the question asker wants :)

Answer 3

ans is 1 if may leap year or not arbecause 52 weeks exist every year so 52 sunday be exist