This was probably true for a bit after 9/11, but I can’t say I personally know anyone who currently feels safer flying on planes because of the TSA. Pretty much everyone I’ve spoken to in person regarding this knows the TSA is a joke.
Realistically it’s now a government jobs program that is basically immune from ever being terminated because many politician benefits from having this program operate in their district/state/etc providing jobs that they do not want to lose.
The gambler’s fallacy is pretty easy to get, as is the Monty Hall problem if you restate the question as having 100 doors instead of 3. But for the life of me I don’t think I’ll ever have an intuitive understanding of the birthday problem. That one just boggles my mind constantly.