Question

The probability that a leap year selected at random will have either $53$ Sundays or $53$ Mondays is:

• A. $\frac{2}{7}$
• B. $\frac{3}{7}$
• C. $\frac{1}{7}$
• D. None of the above

Answer 1

Answer: (B)

$\frac{3}{7}$

$1$ year $=365$ days

A leap year has $366$ days

A year has $52$ weeks. Hence there will be $52$ Mondays for sure.

$52$ weeks $=52\times 7=364$ days

$366-364=2$ days

In a leap year there will be $52$ Mondays and $2$ days will be left.

These $2$ days can be:

Sunday, Monday

Monday, Tuesday

Tuesday, Wednesday

Wednesday, Thursday

Thursday, Friday

Friday, Saturday

Saturday, Sunday

Of these total $7$ outcomes, the favourable outcomes are $3$.

Therefore, the probability that a leap year selected at random will have either $53$ Sundays or $53$ Mondays is $\frac{3}{7}$