This logic is faulty for one reason: it's not a casino with randomly distributed chances. The number of FANG employees is low compared to the entire population,

This logic is faulty for one reason: it's not a casino with randomly distributed chances. The number of FANG employees is low compared to the entire population, yet some of the students are almost guaranteed to make it there, because of their apparent smarts and mindset, while others have about zero chances. So it's a lottery, but the tickets aren't sold to everyone. The same is true for startup founders: some of them are obviously going to make it one day, while others don't even need to apply.