Question

The probability that a leap year selected at random contains either 53 Sundays or 53 Mondays, is

(A) 2/7 

(B) 4/7 

(C) 3/7 

(D) 1/7

Answer 1

Answer is (C) 3/7

A leap year consists of 366 days comprising of 52 weeks and 2 days. There are 7 possibilities for these 2 extra days viz. 

(i) Sunday, Monday, 

(ii) Monday, Tuesday, 

(iii) Tuesday, Wednesday, 

(iv) Wednesday, Thursday, 

(v) Thursday, Friday, 

(vi) Friday, Saturday and 

(vii) Saturday, Sunday.

Let us consider two events : 

A : the leap year contains 53 Sundays 

B : the leap year contains 53 Mondays. 

Then we have

P(A) = 2/7, P(B) = 2/7, P(A ∩ B) = 1/7

 Hence, required probability = P(A ∪ B)

= P(A) + P(B) - P(A ∩ B) = 2/7 + 2/7 - 1/7 = 3/7