## Five Mondays

1. #### David Reynolds:

p(5 Mondays in a month) = 385/4800 = 0.08020833333+ Most common for August or September.

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.

2. #### David Reynolds:

My last post was wrong in a couple of ways. I was only considering months that started with the day in question. And I had February as the wrong month so my leap calculations were off.
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.

3. #### Puzzled:

Can we rely on the Gregorian calendar for this puzzle? If not, which one is to be used?

4. #### J:

It’s trivially 1, but it actually depends.

5. #### David Reynolds:

Another correction.
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.

6. #### tanyakh:

Yes, I meant Gregorian calendar, but I didn’t mention it, because I didn’t want to give a hint. My calculations are the same as the last comment from David.

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