Question

What is the probability that a leap year selected at random will contain $53$ Mondays?

• A. $\frac{2}{5}$
• B. $\frac{2}{7}$
• C. $\frac{1}{7}$
• D. $\frac{5}{7}$

Answer 1

Answer: (B)

$\frac{2}{7}$

A leap year has $52$ weeks (i.e. monday, tuesday ........)

So, there will be $52$ Mondays fixed.
Number of days left $=366-52\times 7=2$
Number of days in last week $=2$
So, the probability of a Monday in the week $=\frac{2}{7}$

Thus, the probability of $53$ Mondays is $\frac{2}{7}$.
Hence, option B is true.