A) \[\frac{2}{7}\]
B) \[\frac{4}{7}\]
C) \[\frac{3}{7}\]
D) \[\frac{1}{7}\]
Correct Answer: C
Solution :
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 \[P(A)=\frac{2}{7},\,\,P(B)=\frac{2}{7},\,\,P(A\cap B)=\frac{1}{7}\] \[\therefore \] Required probability \[=P(A\cup B)\] \[=P(A)+P(B)-P(A\cap B)=\frac{2}{7}+\frac{2}{7}-\frac{1}{7}=\frac{3}{7}.\]
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