UPSC NDA Math Model Paper 8

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