Question

The probability that there will be $53$ Sunday in a year of the $22$nd century chosen at random is :

• A. $\frac{3}{28}$
• B. $\frac{2}{28}$
• C. $\frac{7}{28}$
• D. $\frac{5}{28}$

Answer 1

Answer: (D)

$\frac{5}{28}$

We know, a leap year is fallen within $4$ years, so its probability $=\frac{25}{100}=\frac{1}{4}$
In a century, the probability of $53$ Sunday in a leap year $=\frac{1}{4}\times \frac{2}{7}=\frac{2}{28}$
Non-leap year in a century $=75$
Probability of selecting a non-leap year $=\frac{75}{100}=\frac{3}{4}$
Probability of $53$ Sunday in a non-leap year $=\frac{1}{7}$
Similarly, in a century, probability of $53$ Sunday in a non-leap year $=\frac{3}{4}\times \frac{1}{7}=\frac{3}{28}$
$\therefore$ Required probability $=\frac{2}{28}+\frac{3}{28}=\frac{5}{28}$.