The probability that a leap year selected at random contains either 53 Sundays o

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

Options:

A . 27

B . 47

C . 37

D . 17

Answer: Option C
:
C
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
(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) = \frac{2}{7}, P (B) = \frac{2}{7}, P (A \cap B) = \frac{1}{7}

∴

Required probability =

P (A \cup B)

= P (A) + P (B) - P (A \cup B) = \frac{2}{7} + \frac{2}{7} - \frac{1}{7} = \frac{3}{7}

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