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?


"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


1 comment:

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