If a 31-day month starts on a Friday, Saturday or Sunday it will have 5 Sundays; if not it will have 4. So the probability is 3/7.
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It is a certainty. There will always be at least one month that will meet the requirement.
The simplistic answer is that August will have five Mondays if the month starts on a Saturday, Sunday or Monday. Three days out of the seven so the probability is 3/7 = 0.4286. However, that assumes that any day of the week is equally likely and that is not the case. The impact of leap years and their 2800-year cycle is to increase the probability to 0.43
There are 4 months that end in the letter Y, January, February, May, and July. The probability, then, of a random month ending in the letter Y is 4 in 12, or 1 in 3, or about 0.3333.
There are 12 months to choose from There are 7 months with 31 days in them. The probability of choosing a 31-day month is 7/12.
It is 1. Every month contains 28 days.