I posted this link in a response to another thread, but couldn't find it anywhere else on this site. It's from 2017, posted on SABR.org and compiled by Richard Karcher an Associate Professor at Eastern Michigan and it's insightful relative to the odds of playing and sticking in the MLB.
Being a data geek, I believe the data skewed optimistically regarding the odds of achieving 3 years in the MLB. No database of service time is available or used in determining a 3 year career, a single appearance in 3 different years would count as 3 years in the MLB. In my own data I have found that almost across all rounds roughly 30% of all those that make it to the MLB have careers with less than 20 RBI's (position players) and 20 K's (pitchers). I think it likely that some percentage of this 30% are players that have been up and down across 3 years or more.
There's also a typo in the last data set: Table 12: 12th-20th Rounds
It should be: Table 12: 16th-20th Rounds