Judging the risk

I spent the weekend visiting my daughter at Oberlin College - like all parents, I'm tremendously proud of my children, and find I enjoy spending time with her more than ever.

My return trip was a bit more exciting than usual. After takeoff, the landing gear wouldn't retract, and then the smoke detector in the bathroom went off. The flight attendant commented that the smoke detector had done that on the same plane two days ago, and they replaced parts to try to fix the problem, obviously unsuccessfully. The net result was an emergency landing back at Cleveland, chased down the runway by fire trucks and ambulances. (No one was hurt, and there was no emergency evacuation.)

Several people were unwilling to get back on the plane (which turned out not to matter, since they canceled the flight and rebooked everyone). But it made me wonder - is getting on a plane that's just had an emergency (but a normal landing) safer or riskier than getting on a randomly selected airplane? On the one hand, we know that in this case they had tried and failed to fix the problem several days earlier, which would tend to indicate that it's riskier. [Of course, the problem might be that it's not a failing smoke detector, but something really wrong.] The landing gear issue is different - they hadn't seen that problem before. On the other hand, that particular plane is probably being checked over more carefully than usual by both mechanics and pilots, which would tend to make it less risky.

I've read several articles and books on misperception of risk, but in a simple case like this I don't know how to answer the question. Are people being superstitious in avoiding a flight on a plane that they know had a problem, and instead selecting a plane about which they have no historical information?

Unrelated to the risk item, but while I'm writing, here's my obligatory swipe at TSA: as I went through security, I deliberately did not remove my plastic bag of toiletries from my suitcase, and it went right through without complaints. But the pilot just in front of me had his baggage sent through the scanner twice. As numerous people have pointed out, an insider attack (i.e., a pilot who wants to destroy his own plane in flight) can't be stopped, so there's no point checking their baggage for explosives they placed aboard. I asked him about his feelings on the value of TSA - he didn't want to directly criticize them, but said "I do what I'm told".