Any month of the year is capable of having 5 Mondays. Even February, but that doesn’t happen very often. If you consider all months, then my calculated probability of 1671/4800 = 0.348125 is correct.

But the problem stated that only 31 day months should be included.

Therefore, the probability of 5 Mondays in a 31 day month is 1198/2800 = 0.427857+.

The probability of 5 Thursdays in a 31 day month is 1202/2800 = 0.4292857+ which is the answer to the bonus question.

172 each of January, March, May, October, and December and 171 of July and August in 400 years. ]]>

I now calculate the odd of five Mondays in a month to be 1671/4800 = 0.348125

And I get the same answer for any day of the week. ]]>

I’m puzzled by your bonus question, since I calculate a three way tie:

p(5 Sundays in a month) = 387/4800 = 0.080625. Most common for January, May, or July.

p(5 Tuesdays in a month) = 387/4800 = 0.080625. Most common for January, May, or December.

p(5 Fridays in a month) = 387/4800 = 0.080625. Most common for January, May, or July.