Hi all... the problem that I have difficulties to solve is: Explain why the foll

Question

Hi all... the problem that I have difficulties to solve is:

Explain why the following reasoning is correct or not.

In the days before we had security checks, a frequent flier,concerned
about the possibility of a bomb on a plane, estimates theprobability
of a bomb on a plane to be one in a million. Not satisfied withthe
chances, the person computes the probability of two bombs onthe
same plane to be
(0.000001) 2 = 0.000000000001.

Satisfied with the chances now, the person always carries a bombon
a plane so that the probability of someone else carrying a bomb,and
thus there being two bombs on the plane, is 0.000000000001,small
enough to feel safe.

I hope that someone can help me to solve this problem because Ihave thinked that for solve this we must prove that the events areindependent or not...but I have some problem and I am notsure that is the good way...

Explanation / Answer

It is a case of conditional probability. First, the probability that the plane carries two bombs is(0.000001)2 . Now as we already know that the plane carries one bomb, thenwe should find out the probability that the plane carries in total two bombs given that one bomb isalready on the plane. But then due to independence of events it is same as the probability that the plane iscarrying one bomb, which is again 0.000001

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