Quick Links -    DISC. BOARD   |   Outpost#31 Store   |     
 

- Main Entrance  
- Contact Us
- THING-FEST
- Stewart, B.C. Trip 2003
  Stewart, B.C. Trip 2009
  Cool Stuff
  Collection & Archive
  LINKS
  Our Banners
- DISC. BOARD
   
- Script
- Screenshots
- FAQ's
- Cast & Crew
- Quotes
- Maps and Timeline
- Trivia 
- Goofs
- Special FX
- Behind-the-Scenes
- Deleted Scenes
- DVD
- Technical Specs
- Storyboards
- In Memoriam
 

- Video Game
- Role-Playing Games
- Board Games
   
- Online Articles
- Magazines/Comics
- Books 
- "Who Goes There?"
 
- Fan Fiction Repository
- - Fan Fiction Stories
- - Fan Images
- - Fan Essays
- - Fan Tattoos
     

 

John Carpenter's

 

Blair's Calculation of Infection Probability - Take 2

by Antonio Eleuteri

Steve Crawford’s idea of reproducing the calculations shown in the film is an intriguing one. Unfortunately, the model chosen by Steve is formally not correct for the situation. He seems to assume that Poisson’s distribution has a finite support (i.e. in our case, the outcomes are limited to the 12 persons at the outpost) whereas the theoretical set of outcomes is infinite (from 0 to infinity.) The numbers he got apply to a population infinitely large, i.e. it could be applied to the whole of Earth (if we assume “infinity” as a very large number so that the probability estimates are “close” to the theoretical ones.)

But what happens if we want to use Poisson’s model to the limited population of the outpost? How far off are Steve’s estimates with this approximation? The goodness of the approximation depends on the infection rate.

The correction can be calculated by using the Poisson formula again, for the probability of events larger than 12. For the two extremes of the infection rates, 1.116 and 1.371, these probabilities are 2.38*10^(-10) and 2.73*10^(-9), i.e. of the order of 1 in 1 billion. This means in practice, that the model’s calculations are not affected in practice by the error.

What’s interesting is to calculate the “effective” size of the population to which the model can be applied and still obtain reasonable probabilities. By assuming the largest infection rate of 1.371, the probabilities are as follows:

Minimum

number of

infected

persons

Probability

1

74.61%

2

39.81%

3

15.95%

4

5.05%

5

1.31%

6

0.29%

7

0.055%

 

So we see that the probability decreases quite steeply. So, even if Blair didn’t know much about the rules of probability to apply the “trick” reported by Steve, it would have been enough to apply Poisson’s formula up to 5 or 6 to already get a good estimate.

 

 

 


About Us     Copyright

www.outpost31.com © 2001-2007

contact us