Consider a mind experiment: you are stuck inside a trapped room. There are only two ways for you to go out and you have to choose one. Would you rather go through four traps each with 20% chance of killing you (80% chance to survive each trap), or one trap that has 58% chance of killing you (42% chance to survive the only trap)?
Intuitively I would undoubtedly choose the first option although mathematically I should choose the second option, since mathematically the chances of surviving in the first option is only 40.96%.
Imagining being trapped in such a room, I can easily see myself walk through the four 80% traps one by one without much trouble. But I cannot imagine myself walk through the 42% trap alive without some good luck.
Here are two things I want to know:
- Is my intuition similar to most people or not?
- If this is indeed the most natural intuition, what is the cause that it is different from the mathematical result?