There are many problems with his logic. He wants to reduce his
risk of being blown out of the sky, so he introduces more danger by
bringing his own bomb along. Mr. Paranoid seems to be making the
assumption that the chance of a bomb being on a plane is dependent on the
probability of another bomb also on board the plane. Maybe terrorists
have a monthly convention to make sure that two bombs are not on the same
plane but I don’t think so. Adding another bomb into the exploding plane
scene increases the probability that any given person will be on a plane
with a bomb on it, but by him bringing his own bomb he is guaranteeing a
bomb will be on his plane.
Mr. Paranoid’s biggest problem is that he is looking at the
problem wrong, instead of being afraid of the plane having a bomb on it he
should be afraid of it blowing up. Then he would see that putting a given
bomb on the plane increases the chances of destruction. The probability
of the plane blowing up is dependent on the number of bombs on the plane.
The more bombs on the plane the more likely the plane and all it’s
occupants will come to an untimely death.
I believe Michael Goodie Allot has it right when he claims, P(the
paranoid travelers bomb & some other bomb) = P(paranoid’s bomb) * P(some
other bomb) = 1 * P(some other bomb). This would be true because the two
events are independent and we are given the fact that Mr. Paranoid will
always fly with his bomb. So the probability of having a bomb on the
plane without Mr. paranoid’s bomb is equal to the probability of there
being two bombs on the plane including his given bomb.
Mr. Paranoid would be better off leaving the explosives at home.
Know wonder he is so paranoid, he’s sitting on a bomb. His probability of
dyeing in flight is increased by the bombs mere presents. Even if the
bomb being on the plane decreases the chances of a second bomb is on
board, and the two events aren’t independent of one another, the chances
of one bomb being on his plane are 100%. This should mean danger. The
thing is, the two events are at least 99% independent, with the exception
that he might have bought the last bomb at the airport store, so he would
only be putting himself in more danger. My advice to him as the smartest
man at 10720 woodbine apt #3, would be to go see a psychiatrist and get
rid of the bomb, using the proper method of disposal of course.
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