Question

The probability that there are 53 sundays in a randomly chosen leap year is

• A. $\frac{1}{7}$
• B. $\frac{1}{14}$
• C. $\frac{1}{28}$
• D. $\frac{2}{7}$

Answer 1

The correct option is D $\frac{2}{7}$

Leap year = 366 days = (52 × 7) + 2 days
These two days can be one of the following seven pairs

So sample space S= {Sun - Mon, Mon - Tue, Tue - Wed, Wed - Thu, Thur - Fri, Fri - Sat, Sat - Sun,} = 7 pairs

Favourable cases E= {Sun - Mon, Sat - Sun} = 2 pairs
$HenceP\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}=\frac{2}{7}$