About Fallacy

I find that a frequent problem in academia is fallacy. The fallacies may be so subtle that nobody picks them up. Here are some simple (non-academic) examples of fallacy, so that one may have an idea what fallacies are: 1: The chances that there will be a bomb on my flight are one in a million. The chances that there will be two bombs on my flight are one in a billion. Therefore, I shall be safer if I take a bomb on board. 2: If the Mayoress had personally watered my garden, then my garden would not have died in the summer heat. My garden died in the summer heat. Therefore the Mayoress is personally at fault. (She is! Or can you disprove this?)