A) \[\frac{3}{7}\]
B) \[\frac{2}{7}\]
C) \[\frac{1}{7}\]
D) None of these
Correct Answer: A
Solution :
[a] Since, we know that a leap year contains 52 weeks and 2 odd days. 2 odd days may be (Sunday, Monday), (Monday, Tuesday), (Tuesday, Wednesday), (Wednesday, Thursday), (Thursday, Friday), (Friday, Saturday), (Saturday, Sunday). Let A = event of a leap year containing 53 Saturdays B = event of a leap year containing 53 Sundays. \[\therefore p(A)=\frac{2}{7},\,p(B)=\frac{2}{7}\] and\[P\left( A\cap B \right)=\frac{1}{7}\](According to above odd days possibility) \[\therefore \]Required probability, \[P\left( A\cap B \right)=P\left( A \right)+P\left( B \right)-P\left( A\cap B \right)\] \[=\frac{2}{7}\text{+}\frac{2}{7}\text{+}\frac{1}{7}=\frac{4-1}{7}=\frac{3}{7}\] Hence, option [a] is correct.
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