Question

What is the probability that a leap year has $53$ Sundays?

• A. $\frac{1}{7}$
• B. $\frac{12}{52}$
• C. $\frac{2}{7}$
• D. $\frac{1}{52}$

Answer 1

Answer: (C)

$\frac{2}{7}$

A leap year has $366$ days = $52\times 7+2$ days

That means there will be $52$ Sunday/Monday.../Saturdays plus $2$ additional days. Now these $2$ additional days would be combination of any of the successive two days.

i)Sunday $+$ Monday

ii)Monday $+$ Tuesday

iii)Tuesday $+$ Wednesday

iv)Wednesday $+$ Thursday

v)Thursday $+$ Friday

vi)Friday $+$ Saturday

vii)Saturday $+$ Sunday

Now the probability of two Sundays will be (i) & (vii) $=2$ outcomes out of above $7$ outcomes. So the probability of having two additional Sundays

$=2/7.$