Suppose, I have a machine that accurately gives me the probability of any event occuring.
It's obvious what to do when
- The probabilities are 0.5 and 0.5 (Do nothing)
- The probabilities are 0 and 1 (Remain an atheist)
- The probabilities are 1 and 0 (Become a Muslim)
However, consider a more nuanced scenario. Say I obtained from that machine that the probability of Islam being true is 50.1%, and that the probability of Islam being false is 49.9%. What would you do in this situation? Would you become a Muslim or stay an atheist/agnostic?
Some commenters have raised a very good point. Only taking actions based on probability is not prudent. You have to weigh the consequences too. "If there's a 40% chance of rain, it's still reasonable to take an umbrella, unless carrying the umbrella is an excessive burden." So, it seems like I am just heading towards a traditional Pascal's wager :-)