# If a leap year is selected at random, what is the chance that it will contain 53 Tuesdays?

Question:

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

Solution:

In a leap year, there are 366 days i.e., 52 weeks and 2 days.

In 52 weeks, there are 52 Tuesdays.

Therefore, the probability that the leap year will contain 53 Tuesdays is equal to the probability that the remaining 2 days will be Tuesdays.

The remaining 2 days can be

Monday and Tuesday

Tuesday and Wednesday

Wednesday and Thursday

Thursday and Friday

Friday and Saturday

Saturday and Sunday

Sunday and Monday

Total number of cases = 7

Favourable cases = 2

$\therefore$ Probability that a leap year will have 53 Tuesdays $=\frac{2}{7}$