Actually, your statement was entirely correct. "Let's say 10% of start-ups succeed ... You would need to join 10 of these start-ups ... to have an expectation

Actually, your statement was entirely correct. "Let's say 10% of start-ups succeed ... You would need to join 10 of these start-ups ... to have an expectation of one case [of success]." It is a true statement that the expected number of successes after 10 tries would be 1. It is also a true statement that your chance of zero successes after 10 tries is 34.8%. (The balance comes from the outcomes that include multiple successes.) It may be that the latter is the more relevant and interesting statement to make, but your math was totally right. ;-)