Friday, February 13, 2009

Lucky Strikes

Mathematician Harold Gans made the following calculations:

Ehud Barak stated on January 5, 2009 that 125 Grad-Katyusha missiles "fell on populated areas" of Beersheva, Ashkelon and Ashdod.

Dr. Gans states that he obtained satellite photos and calculated that buildings cover 40% of space in populated areas of these three cities (39.7%, according to the email).

One would expect that if 126 rockets were fell on populated areas, and 40% of the populated areas had buildings, that 50 rockets (40%) would have hit buildings. Barak's announcement stated that only 2% (3 rockets) hit buildings.

If you expect 50 hits, and only 3 actually hit, this seems extraordinarily low. Dr. Gans estimates the odds against this happening as a gazillion to one, or whatever you call a 1 followed by 17 zeros. The calculations for that probability are provided below.

What do you think?


COMMENT FROM A DIFFERENT MATHEMATICIAN:

"I assume it's probably correct. The odds would certainly be minuscule.

The logic is something like this. In the numerator you have the number of ways you can have 1, 2 or 3 missiles landing on the buildings with the associated probabilities. For simplicity, let's assume there is a .4 probability of hitting a building and a .6 probability of missing the buildings.

There are 125 ways only 1 missile lands on buildings. (125 x 124 divided by 2) ways 2 of the missiles hit a building, etc.

125 x .4 x (.6 to the 124th power) +

[(125 x 124) / 2] x (.4 to the 2nd power) x (.6 to the 123rd power) +

[(125 x 124 x 123) / 6] x (.4 to the 3rd power) x (.6 to the 122nd power).

Now in the denominator you have the above cases plus all the other possibilities: 4,5,6.......................or 125 missiles hitting a building.""

Question for your Table
– What’s the difference between “extraordinary good luck” and “miraculous”? Eye of the beholder?


Shabbat Shalom


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