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

Number of days in the month of January in a leap or non-leap year = 31.

There are four complete weeks in the month of January. There are three more extra days in the month. If the month starts on Saturday or Sunday or Monday, there are 5 Mondays in the month of January.

So, the probability of getting 5 Mondays in the month of January (or any month with 31 days) = $\frac{3}{7}$