Before the days of high security at airports, there was a legendary person who was afraid of

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Before the days of high security at airports, there was a legendary person who was afraid of traveling by plane because someone on the plane might have a bomb. He always brought a bomb himself on any plane flight he took, believing that the chance would be astronomically small that two people on the same flight would both have a bomb. Explain the fallacy in his logic, using ideas of independent events and conditional probability.
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