Question

If a leap year is selected at random what is the probability that it will contain $53$ Tuesdays?

• A. $\frac{1}{7}$
• B. $\frac{2}{7}$
• C. $\frac{3}{7}$
• D. $\frac{4}{7}$

Answer 1

Answer: (B)

$\frac{2}{7}$

$1year=365$ days

A leap year has $366$ days

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

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

$366–364=2$ days

In a leap year there will be 52 Tuesdays 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 favorable outcomes are 2.

Hence the probability of getting 53 Tuesdays in a leap year $P\left(E\right)=\frac{2}{7}$