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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:

  1. Is my intuition similar to most people or not?
  2. If this is indeed the most natural intuition, what is the cause that it is different from the mathematical result?
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    $\begingroup$ People play the lottery. Expecting them to act rationally and understand probability is asking a lot. $\endgroup$
    – StrongBad
    Sep 6 '17 at 19:37