Question

What is the probability that a leap year has 52 Mondays?
(a)$\frac{2}{7}$
(b)$\frac{4}{7}$
(c)$\frac{5}{7}$
(d)$\frac{6}{7}$

Answer 1

SOLUTION :

The correct option is (c) : 5/7

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  

Total number of outcomes = 7

Here, we have to make 52 Mondays so the additional days should not include Monday.

Out of these 7 cases , 5 cases have not Monday :{Tue,Wed},{Wed,Thu},{Thu,Fri},{Fri,Sat},{Sat,Sun}

Let E = Event of getting a leap year which has 52 Mondays. .

Number of favourable outcomes to E = 5

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

P(E) = 5/7  

Hence, Probability of getting a leap year which has 52 Mondays , P(E) = 5/7 .

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

A leap year has 52 weeks.So,clearly there are

52 Mondays. The probability is 1.There are 2

extra days in a leap year.The probability that

one of them is Monday is 2/7.So the

probability of 52 Mondays in a leap year is 

1-2/7=5/7.Therefore the probability is 5/7