e are given the probability
that one in a thousand passengers on a plane has a bomb. Assuming that the
probability to have a bomb is evenly distributed among the passengers, the
probability that two passengers have a bomb is roughly equal to
.
Therefore, I take a bomb on a plane to decrease chances that somebody else has
a bomb. What exactly is wrong with this argument?
If I have a bomb then the probability that somebody else has it is the
conditional
probability
by (
Bayes
formula
)
by
independence
Similarly, if I decide not to bring a bomb then I am facing the
probability
Therefore, I don't accomplish anything by bringing a bomb on a plane.
