Here’s a concise answer that straightforwardly applies the rule I already stated. Since my rule only applies above 50% and since P(being shot)=10% (as I recall), then we must consider the negation. Suppose P(I will be shot) is 10% and P(I will be stabbed) is 10% and suppose that (for some reason) “I will be shot” and “I will be stabbed” are mutually exclusive. Since P<50% for each of these we turn it around, and get:
P(I will not be shot)is 90% and P(I will not be stabbed) is 90%. Because the cost of being shot, and the cost of being stabbed, are so very high, then the threshold for being convinced must be very high as well—set it to 99.9%. Since P=90% for each of these, then it does not reach my threshold for being convinced.
Therefore I am not convinced that I will not be shot and I am not convinced that I will not be stabbed. Therefore I will not go without my bulletproof body armor and I will not go without my stab-proof body armor.
So the rule seems to work. The fact that these are mutually exclusive dangers doesn’t seem to affect the outcome. [Added: For what I consider to be a more useful discussion of the topic, see my other answer.]
Here’s a concise answer that straightforwardly applies the rule I already stated. Since my rule only applies above 50% and since P(being shot)=10% (as I recall), then we must consider the negation. Suppose P(I will be shot) is 10% and P(I will be stabbed) is 10% and suppose that (for some reason) “I will be shot” and “I will be stabbed” are mutually exclusive. Since P<50% for each of these we turn it around, and get:
P(I will not be shot)is 90% and P(I will not be stabbed) is 90%. Because the cost of being shot, and the cost of being stabbed, are so very high, then the threshold for being convinced must be very high as well—set it to 99.9%. Since P=90% for each of these, then it does not reach my threshold for being convinced.
Therefore I am not convinced that I will not be shot and I am not convinced that I will not be stabbed. Therefore I will not go without my bulletproof body armor and I will not go without my stab-proof body armor.
So the rule seems to work. The fact that these are mutually exclusive dangers doesn’t seem to affect the outcome. [Added: For what I consider to be a more useful discussion of the topic, see my other answer.]