A man who travels a lot was concerned with the possibility of a bomb on his plane. He determined the probability of this, found it to be low but not low enough for him, so now he always travels with a bomb in his suitcase. He reasons that the probability of two bombs being on board is infinitesimal.
-John Allen Paulos in Innumeracy
Subscribe to:
Post Comments (Atom)
4 comments:
interesting :)
I like :) but really, if he always carries a bomb, doesn't that eliminate him from the probability?
Isn't it true that the probability that both a and b will happen is equal to the probability that b will happen if a will always happen?
If A and B are independent events, the probability of both A and B happening is probability of A happening multiplied by the probability of B happening, i.e p(A)*p(B)
That is different from the probability of B happening given that A happened. If the two events A and B independent then the probability of B given A is the same probability as p(B), because by definition if they're independent one happening shouldn't affect the other.
To give an example, if you're flipping a (fair) coin, the probability of getting heads is 0.5.
The probability of getting heads two times in a row is 0.5*0.5=0.25, that is the probability of getting heads the first time, times the probability of getting heads the second time.
But given that you just flipped the coin once and got heads once does nothing to change the probability of the next time you do it.
That is, given that you just flipped the coin and got heads. The probability of flipping the coin now and getting heads is the same 0.5, because obviously the first flip and the second one are totally independent.
In this man's case, his carrying a bomb is an independent event from a terrorist carrying a bomb. His carrying a bomb does nothing to change the probability of the existence of a terrorist with a bomb on the plane.
Who knows where to download XRumer 5.0 Palladium?
Help, please. All recommend this program to effectively advertise on the Internet, this is the best program!
Post a Comment