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I'll take the 30% chance of success and 10% risk to innocents over the 80% chance of success and 80% risk to innocents or the 0% chance of success. It's still a poor option, but I think it is better than the others.
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The OP asked that the numbers not be changed. He stated that the firing was the only option that could prevent death or serious injury to your family.......
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The choice not to fire will most likely result in the grievous injury or death of yourself or a loved one
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........Under most conditions the gun is the last resort anyway. Once you get to it your other plans have probably failed. Once you get to it you will likely have no time or desire to rationally calculate statistics.