Question

A randomly selected year is containing 53 Mondays then probability that it is a leap year

• A. $\frac{2}{5}$
• B. $\frac{3}{5}$
• C. $\frac{4}{5}$
• D. $\frac{1}{5}$

Answer 1

The correct option is A $\frac{2}{5}$

Selected year will be a non leap year with a probability $\frac{3}{4}$
Selected year will be a leap year with a probability $\frac{1}{4}$
A selected leap year will have 53 Mondays with probability $\frac{2}{7}$
A selected non leap year will have 53 Mondays with probability $\frac{1}{7}$
$E\to$ Event that randomly selected year contains 53 Mondays
$P\left(E\right)=\frac{3}{4}\times \frac{1}{7}+\frac{1}{4}\times \frac{2}{7}=\frac{5}{28}P\left(\frac{leapyear}{E}\right)=\frac{\frac{2}{28}}{\frac{5}{28}}=\frac{2}{5}$