The probability that in a year of $22^{nd}$ century chosen at random, there will be $53$ Sunday, is
A$\frac{3}{28}$
B$\frac{2}{28}$
C$\frac{7}{28}$
D$\frac{5}{28}$
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C$\frac{7}{28}$
We know a leap year is fallen within $4$ years,
So its probability is $\frac{25}{100}=\frac{1}{4}$
$53^{rd}$ Sunday leap year $=\frac{1}{4}\times\frac{2}{7}=\frac{2}{28}$
Similarly probability of $53^{rd}$ Sunday in a non leap year $=\frac{75}{100}\times\frac{1}{7}=\frac{3}{4}\times\frac{1}{7}=\frac{3}{28}$
Required probability $=\frac{2}{28}+\frac{3}{28}=\frac{5}{28}$.
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