A month has 30 days and its 1st falls on a Tuesday. A quiz master writes each date of that month on a slip, mixes the slips and draws one at random. What is the probability that the date drawn is a Sunday?

If the 1st is a Tuesday, the first Sunday is the 6th, and then the 13th, 20th and 27th - four Sundays. $P=\frac{4}{30}=\frac{2}{15}.\frac{1}{7}$ assumes one seventh of a month is Sunday, which is only true when the days divide evenly; $\frac{1}{6}$ counts a fifth Sunday that a 30-day month starting on Tuesday does not have; $\frac{7}{30}$ confuses the 7 days of a week with the count of Sundays.