You are right, you can estimate your probability to stake a block by taking into account the correlation of your weight and the total network weight. Then you can use a binomial distribution calculator to calculate your chances to stake one or another amount of blocks per period. Lets suppose that you have 1% of the total network weight (thus you have a 1% chance to stake the next block) and you want to know how many stakes you can get per day (960 blocks). A resulting graph can look like this (96 tries/10% success probability is used for clarity).


So there is a ~36.5% probability to stake between 11 and 20 blocks per day.
The probability to stake from 1 to 10 times per 960 blocks is respectively ~63.5%.