Question

What is the probability that a leap year has 53 Tuesdays and 53 Mondays?

Answer 1

SOLUTION :

Given :  A leap year

A leap year has  366 days. It  contain 52 weeks and 2  days.

These 2 days can be:

{Sun,Mon}{Mon,Tue},{Tue,Wed},{Wed,Thu},{Thu,Fri},{Fri,Sat},{Sat,Sun}  : 7 cases  

Out of these 7 cases , 1 have Tuesday & Monday : {Mon,Tue}

Let E = Event of getting a leap year which has 53 Tuesdays & 53 Mondays. .

Total number of outcomes =7.  

No.of favourable outcomes= 1

Probability (E) = Number of favourable outcomes / Total number of outcomes

P(E) = 1/7  

Hence, Probability of getting an ordinary year which has 53 Tuesdays & 53 Mondays, P(E) = 1/7 .

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

A leap year has 366 days. Now 364 is divisible by 7 and therefore there will be two excess week days in a 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 have 53 Mondays and 53 Tuesdays . E consists of only one pair in S which is (Monday, Tuesday). So n(E) = 1

Hence, the probability that a leap year will contain 53 Mondays and 53 Tuesdays = n(E)/n(S) = 1/7