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)=27,P(B)=27,P(A∩B)=17 ∴Required probability = P(A∪B) =P(A)+P(B)−P(A∪B)=27+27−17=37
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