Can you find the fallacy in the following joke?
A statistic professor plans to travel to a conference by plane. When he passes the security check, they discover a bomb in his carry-on-baggage. Of course, he is hauled off immediately for interrogation.
"I don't understand it!" the interrogating officer exclaims. "You're an accomplished professional, a caring family man, a pillar of your parish - and now you want to destroy that all by blowing up an airplane!"
"Sorry", the professor interrupts him. "I had never intended to blow up the plane."
"So, for what reason else did you try to bring a bomb on board?!"
"Let me explain. Statistics shows that the probability of a bomb being on an airplane is . That's quite high if you think about it - so high that I wouldn't have any peace of mind on a flight."
"And what does this have to do with you bringing a bomb on board of a plane?"
"You see, since the probability of one bomb being on my plane is , the chance that there are two bombs is . If I already bring one, the chance of another bomb being around is actually , and I am much safer..."