Z is carried off by a tiger. A fires at the tiger knowing it to be likely that the shot may kill Z, but not intending to kill Z and in good faith intending Z's benefit. A's bullet gives Z a mortal wound. A has committed:
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If harm is caused in good faith and with no intent to hurt, no offense is committed.
Step 1: Examine the facts. A fired at the tiger with the aim of protecting Z, not to injure him. Given the absence of intentional harm, A is not guilty of any crime.