You’re checking in at a hotel. Two rooms are available, each with a different fire alarm. The manager tells you that if there’s a fire, you have a 2 percent chance of dying in Room 1. In Room 2, you only have a 1 percent chance.
But…
Room 2′s alarm is squirrelly. Its wiring may cause an electrical fire, which increases your chance of dying in Room 2 by an additional 0.01 percent.
{ 6 comments… read them below or add one }
I’d choose the room with the better view or the farthest from the ice machine. Then open a beer enjoy Monday night football and let the actuaries down the fret about the numbers.
I have to say I hate this problem, and I agree with the commenters at Actuary Info who say that taking Room 1 could be a rational response.
The problem is that the 2% and 1% risks given in the first paragraph are clearly conditional probabilities: “if there’s a fire…” But the 0.01% probability in the second paragraph is associated with the alarm *causing* a fire. As a practical matter, that can’t be a probability conditional on the event of a fire, no matter what the intent of the problem statement was.
I get the point about irrational response to betrayal—there are similar studies showing that people accept higher risk in situations where they feel more in control—but the particulars of this example were, I think, poorly chosen.
You pass.
Yes, but Mr. Patterson gets an A+.
True. Plus, most actuaries would continue arguing the materiality of the conditional probability while the hotel burned around them.
I would have to ask myself why they don’t change the detectors in all the rooms to the better quality (1%) and yet not defective alarms and then go down the road to another hotel. :)