Yes, it is unlikely if we take only one week, but take 30 weeks, and it is not that unlikely anymore, right?
The chance would be only around 9.7%
As already calculated, the chance to not win any lottery ticket in a week is 0.338%. This means that the chance to win at least 1 lottery ticket in a week is 99.662%
Therefore, the chance to have at least 1 week without any lottery ticket in a 30 week period is around 9.7%.
1 - 0.99662
30 = 0.0966