Question

Find the probability that the month of January may have 5 Mondays in

(I) a leap year

(II) a non leap year.

Answer 1

For a leap year and non-leap year there will be 31 days in the month of January
Number of days in a week =7
If 1st of January is a Monday then
1,8,15,22,29
If 2nd of January is a Monday then
2,9,16,23,30
If 3rd of January is a Monday then
3,10,17,24,31
So,
Number of weeks having 5 mondays = 3
Probability = $\frac{3}{7}$