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Question

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

A
27
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B
47
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C
37
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D
17
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Solution

The correct option is C 37
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)=27,P(B)=27,P(AB)=17
Required probability = P(AB)
=P(A)+P(B)P(AB)=27+2717=37

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